Proactively detecting failures on restoration paths in an optical network and visualizations thereof

ABSTRACT

Systems and methods include, responsive to obtaining measurement data from an optical network and determining viability of a plurality of paths based on Signal-to-Noise Ratio (SNR) and availability of the plurality of paths, providing a User Interface (UI) that displays one or more photonic services and a path viability visualization for each of the one or more photonic services, wherein the path viability visualization, for each photonic service, includes visual elements for available paths of the plurality of paths and an indicator associated with each visual element indicative of path viability; and updating the UI responsive to a change in any of the viability and the availability of the plurality of paths. The steps can further include periodically obtaining the measurement data from the optical network and determining the viability of the plurality of paths.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present disclosure claims priority to U.S. Provisional PatentApplication No. 63/047,457, filed Jul. 2, 2020, and entitled “Utilizingan incremental noise metric for rapid modeling of optical networks,” thecontents of which are incorporated by reference in their entirety.

FIELD OF THE DISCLOSURE

The present disclosure generally relates to optical networks. Moreparticularly, the present disclosure relates to systems and methods forutilizing an incremental noise metric for rapid modeling, such asdetermining a Signal-to-Noise Ratio (SNR), of optical networks, and forproactively detecting failures on restoration paths in an opticalnetwork and visualizations thereof.

BACKGROUND OF THE DISCLOSURE

To fully exploit the available capacity within an optical network andefficiently allocate network resources, a real-time tool to accuratelyestimate net system performance is needed. Additionally, for a pluralityof use cases discussed herein, there is a need to determine the localperformance across smaller subsets of the network or within arbitraryconcatenations of fibers and network element objects within any givenpath within the network. One of the more challenging penalties to modelquickly and accurately within the net system performance and as anincremental penalty is the nonlinear interference penalty due to Kerrnonlinearity within the optical fiber. The Gaussian Noise (GN) model hasbeen proposed as a simple model for fiber nonlinearity estimation. Thisis described, for example, in [1] Poggiolini P.: ‘The GN model ofnon-linear propagation in uncompensated coherent optical systems,’Journal of Lightwave Technology, 2012, 30, (24), pp 3857-79; [2]Poggiolini P, Bosco G, Carena A, et al.: ‘The GN-model of fibernon-linear propagation and its applications,’ Journal of Lightwavetechnology,’ 2013, 32, (4), pp. 694-721; [3] Poggiolini P, Bosco G,Carena A, et al.: ‘A detailed analytical derivation of the GN model ofnon-linear interference in coherent optical transmission systems,’ arXivpreprint arXiv:1209.0394, 2012; [4] Carena A, Bosco G, Curri V, et al.:‘EGN model of non-linear fiber propagation,’ Optics express, 2014, 22,(13). pp. 16335-62; and [5] Zhang F, Zhuge Q, Plant DV. Fast analyticalevaluation of fiber nonlinear noise variance in mesh optical networks,IEEE/OSA Journal of Optical Communications and Networking, 2017, 9, (4),pp. C88-97, the contents of each are incorporated by reference herein.

In the literature, there are closed-form solutions for the Incoherent GN(IGN) model, which are sufficiently computationally efficient to allowreal-time nonlinear estimation and can be used to give first orderincremental performance across individual fibers within the network [1].However, these simple closed-form solutions are based on an assumptionof moderately high fiber loss spans, i.e., fiber losses greater thanabout 10 dB, and when these models are used for lower loss spans, thecalculated Nonlinear Interference (NLI) is underestimated. To supportarbitrary loss fiber spans, a more widely applicable method to solve theGN model integrals is required. In practice, there are a large number offibers with low loss and short span length. FIG. 1 is a graph of fiberlength probability distribution of an example optical network. Fiberswith span lengths less than 40 km are approximately 30% of the total.Therefore, any fast estimation tool must provide accurate results forshort, lower loss spans.

Additional shortcomings exist for published methods to calculateincremental penalties within the optical network, where they do notconsider or correct for upstream noise sources or the coherent nonlinearinterference generated by the concatenation of an arbitraryheterogeneous mix of fibers, see, e.g., P. Poggiolini et. al, “The LOGONStrategy for Low-Complexity Control Plane Implementation inNew-Generation Flexible Networks,” OFC 2013, OW1H.3, the contents ofwhich are incorporated by reference herein.

BRIEF SUMMARY OF THE DISCLOSURE

The present disclosure relates to systems and methods for obtaining andutilizing an incremental noise metric for noise localization,performance-based routing, and rapid performance modeling includingreal-time viability monitoring based on metrics such as Signal-to-NoiseRatio (SNR), of optical networks. The present disclosure includes afast, nonlinear estimation process with improved accuracy for low lossspans compared to traditional closed-form GN models, as well as a methodto determine the coherent nonlinear penalty in an arbitraryconcatenation of mixed heterogeneous fibers which is not considered byexisting fast nonlinear interference calculation methods. Thisdisclosure also includes methods to correct the concatenation ofincremental penalties when calculated independently without knowledge ofupstream noise sources, which is a general incremental penaltycorrection applicable to all incoherent noise sources.

In an embodiment, a non-transitory computer-readable storage mediumincludes computer readable code stored thereon for programming aprocessing device to perform steps of obtaining data for a plurality ofelements associated with an optical network; determining an incrementalnoise penalty for each element of the plurality of elements; and storingthe incremental noise penalty for each element of the plurality ofelements. The steps can further include determining Signal-to-NoiseRatio (SNR) across an optical path in the optical network byconcatenating associated incremental noise penalties for each element inthe optical path along with corrections. The corrections can be forupstream incremental noise penalties for elements upstream from theassociated element. The SNR can be determined in real-time based onutilizing stored incremental noise penalties. The SNR for the opticalpath can be utilized as a cost metric in path computation. The steps canfurther include utilizing the SNR for the optical path to determine ifany of a pre-planned restoration route for an optical channel and a newroute for a new optical channel is currently viable. The steps canfurther include identifying sections in the optical network that needmaintenance or repair based on monitoring associated incremental noisepenalties. The steps can further include periodically performing theobtaining, the determining, and the storing; and monitoring theassociated incremental noise penalties over time.

In another embodiment, an apparatus includes one or more processors andmemory storing instructions that, when executed, cause the one or moreprocessors to obtain data for a plurality of elements associated with anoptical network, determine an incremental noise penalty for each elementof the plurality of elements, and store the incremental noise penaltyfor each element of the plurality of elements. The instructions that,when executed, can further cause the one or more processors to determineSignal-to-Noise Ratio (SNR) across an optical path in the opticalnetwork by concatenating associated incremental noise penalties for eachelement in the optical path along with corrections. The corrections canbe for upstream incremental noise penalties for elements upstream fromthe associated element. The SNR can be determined in real-time based onthe stored incremental noise penalties. The SNR for the optical path canbe utilized as a cost metric in path computation. The instructions that,when executed, can further cause the one or more processors to utilizethe SNR for the optical path to determine if any of a pre-plannedrestoration route for an optical channel and a new route for a newoptical channel is currently viable. The instructions that, whenexecuted, can further cause the one or more processors to identifysections in the optical network that need maintenance or repair based onmonitoring associated incremental noise penalties.

In a further embodiment, a method includes obtaining data for aplurality of elements associated with an optical network; determining anincremental noise penalty for each element of the plurality of elements;and storing the incremental noise penalty for each element of theplurality of elements. The method can further include determiningSignal-to-Noise Ratio (SNR) across an optical path in the opticalnetwork by concatenating associated incremental noise penalties for eachelement in the optical path along with corrections. The corrections canbe for upstream incremental noise penalties for elements upstream fromthe associated element. The method can further include utilizing the SNRfor the optical path to determine if any of a pre-planned restorationroute for an optical channel and a new route for a new optical channelis currently viable. The method can further include identifying sectionsin the optical network that need maintenance or repair based onmonitoring associated incremental noise penalties.

In yet another embodiment, a non-transitory computer-readable storagemedium having computer readable code stored thereon for programming aprocessing device to perform steps of, responsive to obtainingmeasurement data from an optical network and determining viability of aplurality of paths based on Signal-to-Noise Ratio (SNR) and availabilityof the plurality of paths, providing a User Interface (UI) that displaysone or more photonic services and a path viability visualization foreach of the one or more photonic services, wherein the path viabilityvisualization, for each photonic service, includes visual elements foravailable paths of the plurality of paths and an indicator associatedwith each visual element indicative of path viability; and updating theUI responsive to a change in any of the viability and the availabilityof the plurality of paths. The steps can further include periodicallyobtaining the measurement data from the optical network and determiningthe viability of the plurality of paths. The steps can further includeproviding a map view of all or part of the optical network, wherein themap view includes nodes and links interconnecting the nodes; andproviding a visualization for each of the links based on a visual key,to indicate a level of the viability thereof. The steps can furtherinclude receiving a selection of a link; and displaying a summary ofcurrent measurement data associated with the link. The viability can bebased on the SNR and whether margin is available thereon, and whereinthe availability is based whether spectrum is available. The indicatorassociated with each visual element indicative of path viability canindicate any of viable, unavailable, current where the photonic serviceis using an associated path, and non-viable. The viability of theplurality of paths based on the SNR can utilize an incremental SNRcomputation. The available paths, for a photonic service, can include ahome path and zero or more standby paths, with a number of visualelements indicating the number of the zero or more standby paths.

In yet another embodiment an apparatus includes a network interface anda processor communicatively coupled to one another; and memory withinstructions that, when executed, cause the processor to, responsive toobtained measurement data from an optical network and determinedviability of a plurality of paths based on Signal-to-Noise Ratio (SNR)and availability of the plurality of paths, provide a User Interface(UI) that displays one or more photonic services and a path viabilityvisualization for each of the one or more photonic services, wherein thepath viability visualization, for each photonic service, includes visualelements for available paths of the plurality of paths and an indicatorassociated with each visual element indicative of path viability: andupdate the UI responsive to a change in any of the viability and theavailability of the plurality of paths. The instructions that, whenexecuted, can further cause the processor to periodically obtain themeasurement data from the optical network and determine the viability ofthe plurality of paths. The instructions that, when executed, canfurther cause the processor to provide a map view of all or part of theoptical network, wherein the map view includes nodes and linksinterconnecting the nodes; and provide a visualization for each of thelinks based on a visual key, to indicate a level of the viabilitythereof. The instructions that, when executed, can further cause theprocessor to receive a selection of a link; and display a summary ofcurrent measurement data associated with the link. The viability can bebased on the SNR and whether margin is available thereon, and whereinthe availability can be based on whether spectrum is available. Theindicator associated with each visual element indicative of pathviability can indicate any of viable, unavailable, current where thephotonic service is using an associated path, and non-viable. Theviability of the plurality of paths based on the SNR can utilize anincremental SNR computation. The available paths, for a photonicservice, can include a home path and zero or more standby paths, with anumber of visual elements indicating the number of the zero or morestandby paths.

In yet a further embodiment, a method includes, responsive to obtainingmeasurement data from an optical network and determining viability of aplurality of paths based on Signal-to-Noise Ratio (SNR) and availabilityof the plurality of paths, providing a User Interface (UI) that displaysone or more photonic services and a path viability visualization foreach of the one or more photonic services, wherein the path viabilityvisualization, for each photonic service, includes visual elements foravailable paths of the plurality of paths and an indicator associatedwith each visual element indicative of path viability; and updating theUI responsive to a change in any of the viability and the availabilityof the plurality of paths. The method can further include periodicallyobtaining the measurement data from the optical network and determiningthe viability of the plurality of paths. The method can further includeproviding a map view of all or part of the optical network, wherein themap view includes nodes and links interconnecting the nodes; andproviding a visualization for each of the links based on a visual key,to indicate a level of the viability thereof. The method can furtherinclude receiving a selection of a link; and displaying a summary ofcurrent measurement data associated with the link.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is illustrated and described herein withreference to the various drawings, in which like reference numbers areused to denote like system components/method steps, as appropriate, andin which:

FIG. 1 is a graph of fiber length probability distribution of an exampleoptical network;

FIG. 2 is a flowchart of a process that, for a given optical networkstate, provides steps taken in a polling-based approach to determine theincremental NSR for the elements in the optical network;

FIG. 3 is a diagram of the definition of an Additive-White-GaussianNoise (AWGN)-producing element;

FIGS. 4 and 5 are graphs illustrating nonlinear Noise-to-Signal ratio(NSR) for a channel at 1550 nm versus the number of spans using theproposed Fast Coherent Gaussian Noise (FCGN), Incoherent GN model (IGN),and the conventional model over a homogeneous link with uniform symbolrate and channel spacing;

FIG. 6 is a similar graph as FIGS. 4 and 5 over a random heterogeneouslink;

FIG. 7 is a graph of the distribution of span losses in typicalnetworks;

FIGS. 8(a) and 8(b) are graphs of Nonlinear NSR for NDSF (FIG. 8(a)) andTWC (FIG. 8(b)) under different span lengths;

FIGS. 9(a)-9(c) are graphs of the convergence rate of IGN MC and IGN QMCfor NDSF with 30 km (FIG. 9(a)), NDSF with 80 km (FIG. 9(b)), and TWCwith 80 km (FIG. 9(c));

FIGS. 10(a) and 10(b) are graphs of the Delta NSR (the differencebetween IGN and SSFM) with 16 QAM for NDSF (FIG. 10(a) and TWC (FIG.10(b);

FIG. 11 is a flowchart of a process of utilizing an incremental noisemetric for rapid modeling of optical networks;

FIG. 12 is a network diagram of an example optical network;

FIG. 13 is a network diagram of another optical network illustratingadditional details of photonic control and an SDN controller;

FIG. 14 is a block diagram of a processing device, which may be used toimplement the SDN controller, the management system, the in-skincontroller, a user device, any of the process described herein, etc.;

FIG. 15 is a screenshot of a photonic performance dashboard;

FIGS. 16-18 are screenshots of a fiber span performance map,illustrating various features:

FIGS. 19 and 20 are screenshots illustrating expansion of the photonicperformance dashboard illustrating a photonic service path viabilityvisualization;

FIGS. 21, 22, and 23 are screenshots of a map and details of thephotonic service selected in the path viability visualization of FIG.20; and

FIG. 24 is a flowchart of a process for optical path viabilityvisualization.

DETAILED DESCRIPTION OF THE DISCLOSURE

Again, the present disclosure relates to systems and methods forobtaining and utilizing an incremental noise metric for noiselocalization, performance-based routing, and rapid performance modelingincluding real-time viability monitoring based on metrics such asSignal-to-Noise Ratio (SNR), of optical networks. The present disclosureincludes a fast, nonlinear estimation process with improved accuracy forlow loss spans compared to traditional closed-form GN models, as well asa method to determine the coherent nonlinear penalty in an arbitraryconcatenation of mixed heterogeneous fibers which is not considered byexisting fast nonlinear interference calculation methods. Thisdisclosure also includes methods to correct the concatenation ofincremental penalties when calculated independently without knowledge ofupstream noise sources, which is a general incremental penaltycorrection applicable to all incoherent noise sources.

§ 1.0 Incremental SNR and NSR

The metric that dictates the capacity of a channel is theSignal-to-Noise Ratio (SNR), where the maximum capacity achievable isgiven by the Shannon-Hartley theorem. The present disclosure proposesthe use of incremental SNR (or equivalently the inverse of SNR, namelythe Noise-to-Signal Ratio (NSR)) as a pre-computed and stored metric tocharacterize elements of an operating optical network, which can beconsumed for various uses. In linear units, there is a reciprocalrelationship between the NSR and the SNR and that knowledge of one issufficient to define the other. For any element in an optical path(e.g., fiber, an Erbium-Doped Fiber Amplifier (EDFA), etc.), it ispossible to describe the incremental penalty of that object by anincremental NSR at a given frequency, in a given state by:

$\begin{matrix}{{{\Delta\;{{NSR}(v)}} \equiv {{{NSR}_{out}(v)} - {{NSR}_{in}(v)}}} = \frac{\Delta{N(v)}}{S_{out}(v)}} & (1.1)\end{matrix}$

Where:

The state of the optical network is defined by the expected powerspectral profiles at each point, the gain settings of each amplifier,the losses of each fiber, etc.;

ΔN is the equivalent additive noise of the element referenced at theoutput of the element in linear units (e.g., mW) within a givenbandwidth. Again, elements are in the optical network and can include,without limitation, fibers, amplifiers, Wavelength Selective Switches(WSS), gain flattening filters, Variable Optical Attenuators (VOAs),Optical Add/Drop Multiplexers (OADMs), and the like; and

S_(out) is the signal power at the output of the element in linear units(e.g., mW) typically within the same bandwidth as ΔN, which is nominallythe bandwidth of a channel of interest.

The ΔN parameter can be due to various equivalent noise sources acrossthe element, including Amplified Spontaneous Emission (ASE) and KerrNonlinear-Interference (NLI).

A concatenation of elements describes a path in the optical network,such as an Optical Multiplex Section (OMS), where each element hasapproximately independent noise sources will have an incremental NSRsimply described by the sum of each of their incremental NSRs, which isobvious from the definition of incremental NSR above:

$\begin{matrix}{{\Delta\;{{NSR}_{ensemble}(v)}} = {\sum\limits_{k}{\Delta\;{{NSR}_{k}(v)}}}} & (1.2)\end{matrix}$

The aspect of approximately independent noise sources is the case formost elements in an optical path, apart from some older low dispersionfibers, which can be addressed with a coherent correction. This meansthe path SNR, which is directly convertible into maximum achievablecapacity, can be immediately obtained as simply the inverse of the sumof all incremental NSRs within a path.

For concatenating incremental NSRs, first, the incremental NSR of agiven element depends on the output signal power, and, therefore,depends on the concatenated incremental NSR of all elements preceding agiven element (since the equivalent noise from all upstream elementsmust be removed). This may seem contradictory at first in that it is notpossible to know the exact incremental NSR of a given element “in avacuum” without knowing the incremental NSR of all preceding elements;however, if the power state of the network defined by system controlobjectives is approximately known, it is possible to assume any inputNSR to when evaluating an element and correct for it using thetechniques described in § 3.0 Incremental NSR Correction.

Second, the incremental NSR of a concatenation of fibers will have acoherent penalty due to the interaction between fibers. This can becorrected using the techniques described in §§ 4.0 and 5.0.

§ 1.1 Process for Determining Incremental NSR

FIG. 2 is a flowchart of a process 10 that, for a given optical networkstate, provides steps taken in a polling-based approach to determine theincremental NSR for the elements in the optical network. This isdescribed as a polling-based approach but could be implemented based onstate change instead as well as in addition to. Of course, otherembodiments are also contemplated with the process 10 presented forillustration purposes. The process 10 starts (step S1) based on thepolling-based approach, i.e., after a certain period, automaticallyimplemented, manually implemented. In a state changed-based approach,the process 10 can start after a network change, e.g., topology change,capacity change, etc.

The process 10 includes a determination if there has been a physicaltopology change in the network (step S2), meaning one or more elementshave been added, removed, changed, etc. If so (step S2), the process 10includes the collection and generation of fixed data (step S3). If therehas been no physical topology change (step S2) or after the collectionand generation of fixed data (step S3), the process includes collectionof varying network element data (step S4). The process 10 includes adetermination if the data has changed (step S5), namely the datacollected in steps S3, S4. If the data has changed (step S5), theprocess 10 includes calculation and storage of the incrementalpenalties, i.e., incremental NSR for each element (step S6). If the datahas not changed (step S5) or after the step S6, the process 10 includesa delay (step S7) until the next iteration is performed.

Additional details for the associated steps are described. For thecollection and generation of fixed data (step S3), this includes datasuch as factory calibration data, fiber characteristics, etc. and itonly needs to be captured once until the physical topology of the systemchanges. This could be a collection of information such as EDFAcharacteristics (noise figure, ripple, dynamic gain tilt, etc.) as wellas fiber characteristics such as length, loss, fiber type (or fibercharacteristics. For example, fiber characteristics may be collected asdescribed in PCT Patent Application PCT/US20/25177, filed Mar. 27, 2020,and entitled “Optical fiber characterization using a nonlinear skirtmeasurement,” the contents of which are incorporated by reference intheir entirety. The collection and generation of fixed data (step S3)provide the physical parameters required to model the physical behaviorof the optical system. This step can also include generation ofintermediate parameters which are expensive to calculate once based onother fixed data but can be stored and reused in future calculations,such as nonlinear coupling coefficients described in § 6.0 as ϕ_(m,n).

For the collection of varying network element data (step S4), this caninclude Performance Monitoring (PM) data, such as power, power spectrum,gain state of EDFAs, etc., which can vary over time due to perturbations(e.g., fiber pinch changing loss). This PM data is collected to capturethe current state of the network—this step could also include defining astate of the network which is not currently present including simulatedelements that are not currently available or an anticipated future stateof the existing network (e.g., different channel density conditions).

For the calculation and storage of the incremental penalties (step S6),this is performed on a per OMS basis, but the incremental SNR resultsare on more granular elements (e.g., amplifiers, fibers, etc.). The OMSin an optical network is an all-optical link between OADM elements. TheOMS includes various elements, but the channel capacity is fixed alongan OMS since there are no elements to add/drop channels within the OMS.The calculation and storage of the incremental penalties (step S6)include a determination of the power state of the network per OMS (powerspectrum or expected power spectrum at every node in the network) by:

Forward modeling transfer functions of different elements (e.g.,Wavelength Dependent Loss (WDL) and Stimulated Raman Scattering (SRS) infiber, such as described in Han, Qun, et al. “Novel shooting algorithmfor highly efficient analysis of fiber Raman amplifiers.” Journal ofLightwave Technology 24.4 (2006): 1946-1952, the contents of which areincorporated by reference herein, and the gain transfer function inEDFAs due to homogeneous and inhomogeneous broadening such as describedin Bolshtyansky, Maxim. “Spectral hole burning in erbium-doped fiberamplifiers. Journal of Lightwave Technology 21.4 (2003): 1032-1038. thecontents of which are incorporated by reference herein, plus any lumpedlosses or filter shapes); and

Backward error correction when spectral information is available (i.e.,by comparing the forward modeled spectral information with any availablespectral monitors and within the OMS, typically at the output anddistributing the error between forward model and direct measurement backonto elements within the OMS).

The calculation and storage of the incremental penalties (step S6)further include calculating the incremental NSR of each element atselected frequencies as:

$\begin{matrix}{{\Delta\;{NSR}_{ASE}} = \frac{\Delta\; N_{ASE}}{S_{out}}} & ( {1.3a} ) \\{{\Delta\;{NSR}_{NLI}} = \frac{\Delta\; N_{NLI}}{S_{out}}} & ( {1.3b} ) \\{{\Delta\;{NSR}} = {{{\Delta\;{NSR}_{ASE}} + {\Delta\;{NSR}_{NLI}}} = \frac{{\Delta\; N_{ASE}} + {\Delta\; N_{NLI}}}{S_{out}}}} & ( {1.3c} )\end{matrix}$

Where at this point, all the values are known from the previous step. Inthe case of EDFAs,

ΔN _(ASE) =hνΔν(G·NF−1)  (1.4)

Where: h is Planck's constant, ν is frequency, Δν is the bandwidth ofintegration, G is the amplifier gain (linear) at frequency ν which isknown from the EDFA modeling, and NF is the amplifier noise figure atfrequency ν and is typically available from factory calibration orstatistical data known to the network equipment provider (as a functionof amplifier state which is also known). ΔN_(NLI) is typically smallenough to be neglected, or in the case of L-band EDFAs may becharacterized as a function of the EDFA state and stored on the devicewith calibration data, much like noise figure.

In the case of fibers, including Raman amplified fibers, ΔN_(ASE) can befound by solving the differential equations described in Han, Qun, etal. “Novel shooting algorithm for highly efficient analysis of fiberRaman amplifiers.” Journal of Lightwave Technology 24.4 (2006):1946-1952, for example, and ΔN_(NLI) is described in §§ 4.0 and 5.0, forexample.

At the outcome of the process 10, the incremental NSR penalties arestored. Once the incremental NSR (or equivalently SNR) is captured for agiven set of network states of interest, they can be consumed forvarious use cases as now described.

§ 2.0 Use Cases § 2.1 Rapid Path Performance Calculation

In both network planning and operation, there are numerous cases wherethe rapid computation of a path performance is useful. For example, thiscan be used in real-time path viability determinations. As describedherein, real-time means the processes are quick and able to provideresults in seconds. The rapid performance modeling can be applied tocurrent data (real-time or near real-time) as well as historicaldata—seconds, hours, or any older data. The real-time path viabilitydeterminations can determine if planned restoration routes are viablebased on current conditions of the network (i.e., “Restoration injeopardy” tracking). The real-time path viability determinations can beused to make in-situ decisions on which path to route on based on thebest current performance by simultaneously tracking multiple possiblerestoration routes. As is known in the art, in-situ means local such asa local decision by a network element performing path computation. Otheruse cases can include higher-level applications (e.g., Routing,Modulation, and Spectrum Assignments (RMSA) decision making forrouting). Also, planning tools can utilize the techniques describedherein for network planning purposes.

§ 2.2 SNR-Based Routing

Path computation is performed to determine a path or route through theoptical network for a demand and decides the path based on the state ofthe network and costs. Current routing decisions are often made based onminimizing path length (as the cost), for example, but the performanceis ultimately dictated by the SNR, not proxy metrics like the length.The incremental SNR/NSR lends itself extremely well to make decisionsbased on routing since it is a straightforward input into acost-function or can be directly utilized as the cost. A PathComputation Engine (PCE) utilizing Dijkstra or similar algorithm couldconsume the incremental NSRs to determine the lowest cost (best SNRperformance) directly, rather than using proxy cost metrics. A keyaspect is the incremental NSR calculation is real-time and thus providesbetter data than proxy cost metrics without the disadvantage ofcalculation time and power.

§ 2.3 Noise Localization

Visibility of the incremental SNR/NSR gives direct information about thelocal performance of individual elements (spans, amplifiers, sections,etc.) of the network. It is possible to look at individual spans or OMSsto see which areas are contributing better or worse performance both inrelative (e.g., relative to planning) or absolute terms. In observingperformance relative to planning, this can be extremely useful indebugging network performance by finding which spans/sections, etc. areout of specification if a path is not performing as expected. Theabsolute incremental SNR/NSR numbers for given spans/sections can beused to qualify each other against the other spans/sections in thenetwork which can be used to prioritize repair and maintenance (for theworst-performing parts of the network) or to make routing decisions asdiscussed above, for example.

§ 2.4 Monitoring System Performance Variation Over Time

By monitoring the incremental SNR/NSR variation throughout the network,this provides a better idea of the overall network performance variationover time. As an example, an operator may currently track powervariation over time, and where a 3 dB variation may raise concerns, butthat may translate to a small added penalty in terms of the incrementalSNR/NSR in absolute units such that it would not affect a channelpassing through that set of elements noticeably. On the other hand, somesmaller power variation elsewhere in the network may trigger a largeadditional incremental SNR/NSR penalty, which would affect channelspassing through those elements, and it is better to focus on theseareas. That is, the incremental SNR/NSR is a much better and usefulmetric in terms of absolute network performance.

§ 2.5 Optimization Using APIs

By regularly tracking the incremental SNR/NSR across different elementsin the network (and possibly for different network statessimultaneously), the data could be consumed by a large number ofdifferent higher-layer applications, via Application ProgrammingInterfaces (APIs). That is, the tracking of the incremental SNR/NSRacross different elements can be at the network element level and/or atthe management level, and this data can be advertised, via APIs, toother applications. Some example applications can include 1) variablebandwidth restoration applications (e.g., find protect routes that havedifferent bandwidth values as working routes), 2) bandwidth optimizationapplications, 3) path viability applications (tracking plannedrestoration route performance before channels are moved), 4) maintenanceand repair prioritization applications, 5) RMSA utilizing SNR-basedrouting, 6) defragmentation applications (e.g., moving existing channelsto better SNR paths, to improve the overall state of the network).

§ 3.0 Incremental NSR Correction

Adding incremental NSRs of Additive-White-Gaussian Noise-producing(AWGN-producing, or approximately AWGN-generating) elements is aconvenient way to determine the total penalty of a concatenation of suchelements. The issue is that the noise from upstream objects changes theincremental NSR of a given element downstream. For this reason, it isnot possible to evaluate incremental NSRs independently and add themtogether without some form of correction. The correction to thisanalysis is described in this section.

FIG. 3 is a diagram of the definition of an AWGN-producing element. Anarbitrary AWGN-producing element or concatenation of AWGN-producingelements can be modeled as in FIG. 3 at a given frequency, within agiven bandwidth:

S _(out) =G·S _(in)  (3.1)

N _(out) =G·N _(in) +ΔN  (3.2)

where

-   -   P_(in/out)=S_(in/out)+N_(in/out) is total input/output power        (linear units)    -   G is the element gain (linear units)    -   S_(in/out) is the input/output signal power (linear units)    -   N_(in/out) is the input/output noise power (linear units)    -   ΔN is the additive AWGN power of the element referenced at the        output (linear units)

The incremental NSR of an AWGN-producing element or concatenation ofAWGN-producing elements is given by

$\begin{matrix}{{\Delta\;{NSR}} = {{{NSR}_{out} - {NSR}_{in}} = {{\frac{N_{out}}{S_{out}} - \frac{N_{in}}{S_{in}}} = {{\frac{{G \cdot N_{in}} + {\Delta\; N}}{G \cdot S_{in}} - \frac{G \cdot N_{in}}{G \cdot S_{in}}} = {\frac{\Delta\; N}{G \cdot S_{in}} = \frac{\Delta\; N}{S_{out}}}}}}} & (3.3)\end{matrix}$

Where it is noted that the incremental NSR is proportional to theinverse of the input signal power within a given bandwidth only, not thetotal input power within a given bandwidth.

If one were to evaluate the incremental NSR penalty of an elementwithout knowing what came before that object, one is forced to make someassumption about the input NSR into our element under investigation. Ifthe input assumed NSR of an element is incorrect, the calculatedincremental NSR of that element will also be incorrect and thus cannotbe concatenated directly with other elements incremental NSRs. Assumingthe total power was correct in evaluating the calculated incrementalNSR*, one can find the corrected incremental NSR penalty by simplyscaling by the correct input signal power:

$\begin{matrix}{{\Delta\;{NSR}_{corr}} = {\Delta\;{{NSR}_{calc} \cdot \frac{S_{{in},{calc}}}{S_{{in},{corr}}}}}} & (3.4)\end{matrix}$

The input signal power can be rewritten in terms of total power in inputNSR as:

$P_{in} = {{S_{in} + {N_{in}\mspace{14mu}{and}\mspace{14mu}{NSR}_{in}}} = { \frac{N_{in}}{S_{in}}arrow S_{in}  = \frac{P_{in}}{1 + {NSR}_{in}}}}$

Rewriting the equation (3.4) (where we note the assumption that thetotal input power was correct):

$\begin{matrix}{{\Delta\;{NSR}_{corr}} = {\Delta\;{{NSR}_{calc} \cdot \frac{1 + {NSR}_{{in},{corr}}}{1 + {NSR}_{{in},{calc}}}}}} & (3.5)\end{matrix}$

In the case where it is assumed that all input power is signal power(typical case), the correction becomes simply:

ΔNSR_(corr)=ΔNSR_(calc)·(NSR_(in,corr)+1)  (3.6)

This is simply a recursive function to generate correct incremental NSRsper element which can then be added in the usual way:

Function [dNSR_corr, dNSR_tot] = correctAndConcatenateNSRs(dNSR_calc,NSR_in) dNSR_corr(1) = dNSR_calc(1)*(NSR_in + 1); For idx = 2:numEldNSR_corr(idx) = dNSR_calc(idx)*(sum(dNSR_corr(1:idx−1))+1); EnddNSR_tot = sum(dNSR_corr); END

§ 4.0 Rapid Optical Communication Path Viability Determination Enabledby Simplified Coherent Nonlinear Interference Estimation

In an embodiment, the present disclosure includes a process toefficiently and accurately determine physically viable opticalcommunication paths. This process could be used in concert with pathranking algorithms to quickly perform live optimal Layer 0 restorationsin a mesh network without having to pre-plan for restoration paths (orgreatly reduce the amount of planning required) and in determiningperformance costs in RMSA algorithms. The process uses modularcalculated values of incremental SNR due to ASE, and other linepenalties for each element (which can be stored for later use), and byhaving a rapid coherent nonlinear penalty calculator, it is possible tocalculate the SNR margin of an arbitrary path fast enough that it couldbe used to make real-time system path viability decisions (e.g.,sub-second total computation, versus multiple minutes to hours forexisting approaches).

In an embodiment, a process is described to efficiently and accuratelydetermine physically viable paths in an optical network in terms of theavailable contiguous frequency spectrum to support a given baud rate,and in terms of SNR performance to support the desired line-rate for agiven modern technology which is present in the network. The SNRperformance can be inferred from measured network data, including powermonitors, power spectrum monitors, and SNR, as reported by opticalmodems. Also, the SNR performance can be inferred from modeled networkbehavior (i.e., modeled linear and nonlinear performance penalties).

Current approaches of determining viable paths are performed withoffline computing resources and do not meet the computation timerequirements be performed dynamically within the network, or by anin-skin orchestrating layer. The determination of viable paths istypically done using offline modeling tools, which require longsimulation times largely due to the long computation times of nonlinearpenalties. That is, the current approaches are computationally complex,requiring significant time.

In optical network planning and design, physics-based modeling tools areused to determine path impairments to make decisions about how to routechannels, which guarantees performance. The present disclosure providesa simple method to quickly determine optical communication pathviability and performance much faster than traditional techniques. Thepresent disclosure uses a simple, coherent NLI model. This could beapplied to both:

1) Significantly reduce time spent in system design/network planning,and more critically, and

2) Make real-time path viability decisions (e.g., in the case of a fibercut or other failure, it is possible to determine an optimal path tore-route to dynamically—current techniques require designatedrestoration paths and are thus less adaptive, and more complex to designaround).

One of the impairments required to model, which is difficult to computeboth quickly and accurately, is the NLI penalty due to the Kerr effect.The procedure to determine this penalty involves solving the NonlinearSchrödinger Equation (NLSE) which could be done, for example, using aSplit-Step Fourier (SSF) technique which is very accurate but also verycomputationally expensive, which leads to computation times which arefar too long for real-time path viability determination.

Over the past several years, a Gaussian Noise (GN) model has risen toprominence in academic literature for modeling NLI, whereby the NLI iscomputed assuming all power sources are GN, which typically gives anupper bound estimate of the amount of NLI that would be generated(again, see, e.g., Poggiolini, Pierluigi. “The GN model of non-linearpropagation in uncompensated coherent optical systems,” Journal ofLightwave Technology 30, no. 24 (2012): 3857-3879), Poggiolini,Pierluigi, G. Bosco, A. Carena, V. Curri, Y. Jiang, and F. Forghieri,“The GN-model of fiber non-linear propagation and its applications,”Journal of Lightwave Technology 32, no. 4 (2014): 694-721, andPoggiolini, Pierluigi, Gabriella Bosco, Andrea Carena, Vittorio Curri,Yanchao Jiang, and Fabrizio Forghieri, “A detailed analytical derivationof the GN model of non-linear interference in coherent opticaltransmission systems,” arXiv preprint arXiv:1209.0394 (2012), thecontents of each are incorporated herein by reference.

This makes the GN model a safe technique to estimate NLI as aperformance penalty, since it is usually very close to reality and, ifit is wrong, it is pessimistic in modeled performance. The difficultywith the GN model is the complete form equation remains very complex tosolve, which is why the typically used equations in literature makenumerous assumptions and/or approximations to simplify the functionalform. The most common assumptions are that all fibers in a path have thesame characteristics (length, type, etc.) and that discrete amplifiersexactly compensate for the loss of a preceding fiber. Theseapproximations work well in many submarine optical deployments but arevery unrealistic in most terrestrial systems, which limits the realisticapplication space of the GN model.

The nonlinear noise to signal ratio (NSR_(NL)) as computed by the GNmodel, can conveniently be separated into two parts which sum together,which are the incoherent contribution and coherent contribution:

NSR_(NL,n)(N _(s))=NSR_(NL,n) ^(IC)(N _(s))+NSR_(NL,n) ^(cc)(N_(s)),  (4.1)

Where NSR_(NL,n) ^(IC)(N_(s)) is the incoherent contribution of the NLIgenerated on the n^(th) channel due to the N_(s) spans in the path, andNSR_(NL,n) ^(cc)(N_(s)) is the coherent contribution of the NLIgenerated on the n^(th) channel due to all spans between the first andN_(s) ^(th) span in the path. With some reasonable approximations of asurface shape to integrate over, the first part of this equation has aclosed-form analytic solution:

$\begin{matrix}{{{{NSR}_{{NL},n}^{IC}( N_{s} )} = {{\sum\limits_{k = 1}^{N_{s}}{\sum\limits_{{m = 1},{m \neq n}}^{N_{ch}}{\frac{8}{27}\frac{{\gamma_{m}^{2}(k)}{L_{{eff},m}^{2}(k)}{\alpha_{m}(k)}{P_{m}^{2}(k)}}{{{\pi\beta}_{2,m}(k)}B_{{ch},m}^{2}}\{ {{{asinh}( {\frac{\pi^{2}{\beta_{2,m}(k)}B_{{ch},m}}{\alpha_{m}(k)}\lbrack {( {f_{m} - f_{n}} ) + \frac{B_{{ch},m}}{2}} \rbrack} )} - {{asinh}( {\frac{\pi^{2}{\beta_{2,m}(k)}B_{{ch},m}}{\alpha_{m}(k)}\lbrack {( {f_{m} - f_{n}} ) - \frac{B_{{ch},m}}{2}} \rbrack} )}} \}}}} + {\frac{8}{27}\frac{{\gamma_{n}^{2}(k)}{L_{{eff},n}^{2}(k)}{\alpha_{n}(k)}{P_{n}^{2}(k)}}{{{\pi\beta}_{2,n}(k)}B_{{ch},n}^{2}}{{asinh}( \frac{\pi^{2}{\beta_{2,n}(k)}B_{{ch},n}^{2}}{2{\alpha_{n}(k)}} )}}}},} & (4.2)\end{matrix}$

Where

P_(m)(k) is m^(th) channel power at the beginning of k^(th) span,

B_(ch,m) and f_(m) are bandwidth and central frequency for channel m,respectively,

L_(s,m)(k) and L_(eff,m)(k) are span length and effective length forchannel m at k^(th) span, respectively, and

γ_(m)(k), β_(2,m)(k) and α_(m)(k) are nonlinear coefficient,second-order dispersion coefficient, and attenuation coefficient forchannel m at k^(th) span, respectively.

The second part of the equation (4.1) which is NSR_(n) ^(CC)(N_(s)) doesnot have a simple or generic form published in the literature. This is alarge part of what is addressed herein. By recognizing the Self-PhaseModulation (SPM) term was the dominant term in the coherentcontribution, a simple and generic coherent contribution term isderived, which can be applied in mixed baud-rate, mixed fiber(heterogeneous) systems where other simplified GN models are notapplicable.

The coherent contribution can then be written as:

$\begin{matrix}{{{NSR}_{{NL},n}^{CC}( N_{s} )} = \{ \begin{matrix}\begin{matrix}{\frac{16}{27}{\sum\limits_{N_{s}^{\prime} = 2}^{N_{s}}{{\gamma_{n}( N_{s}^{\prime} )}{L_{{eff},n}( N_{s}^{\prime} )}{P_{n}( N_{s}^{\prime} )}}}} \\{{\sum\limits_{k = 2}^{N_{s}^{\prime} - 1}\frac{{\gamma_{n}(k)}{L_{{eff},n}(k)}{P_{n}(k)}}{\pi\;{\tau_{{CD},n}( {k,N_{s}^{\prime}} )}B_{{ch},n}^{2}}},}\end{matrix} & {N_{s} > 1} \\{0,} & {N_{s} = 1}\end{matrix} } & (4.3) \\{{\tau_{{CD},n}( {k,N_{s}} )} = {\sum\limits_{l = k}^{N_{s} - 1}{{\beta_{2,n}(l)}{L_{s,n}(l)}}}} & (4.4)\end{matrix}$

For brevity in the remainder of this document, this is referred to asthe combined simplified NLI model as FCGN for “Fast Coherent GN” model.

§ 4.1 Efficacy of Model

To demonstrate the accuracy of the FCGN, simulation line-ups wereperformed against a conventional model that models propagationimpairments through a combination of an SSF solver (SPM) and proprietarynon-linear Wavelength Division Multiplexing (WDM) estimators (Four-WaveMixing (FWM), Cross-Phase Modulation (XPM), Cross-PolarizationModulation (XPoIM)).

In addition, the results as solved are plotted by only considering theincoherent part of the GN model since this process could also beconsidered for arbitrary heterogeneous fiber systems.

FIG. 4 illustrates NSR for a channel at 1550 nm versus a number of spansfor 56/200 Gbps transmitter with 3 dBm launch power and 56/400 Gbpstransmitter with 0 dBm launch power over NDSF. The span length is 80 km.The system is 64 channels with 75 GHz channel spacing. The right graphis the zoom in the left graph. FIGS. 4 and 5 investigate nonlinearNoise-to-Signal ratio (NSR) for a channel at 1550 nm versus the numberof spans using the proposed Fast Coherent Gaussian Noise (FCGN),incoherent GN model (IGN), and the conventional model over a homogeneouslink with uniform symbol rate and channel spacing. In both FIGS. 4 and5, a 64-channel WDM system using 56 GBd transceivers with 75 GHz channelspacing is modeled. In FIG. 4, the channels are sent over 80 km spans ofNon-Dispersion Shifted Fiber (NDSF) fiber, where one plot corresponds toa line rate of 200 Gbps, and another plot corresponds to a line rate of400 Gbps. In FIG. 5, the channels are sent over 80 km spans of TruewaveReduced Slope (TWRS) fiber with a line rate of 200 Gbps.

The plots in FIGS. 4 and 5 show that the FCGN is always slightlypessimistic in NSR performance when compared with the conventional model(i.e., the nonlinear penalty is overestimated), but converges with theconventional model when the signal looks more like Gaussian noise eitherby having high cardinality modulation formats or passing through enoughnet dispersion or a combination of the two effects. For the abovereasons, the results between FCGN and the conventional model convergefaster on NDSF fiber (due to higher dispersion compared to TWRS), andeven faster on NDSF when using 400 Gb/s. This is contrary to an IGNmodel, which diverges with the conventional model at high span counts,where the IGN performance becomes optimistic compared to theconventional model. This is the expected behavior of a complete GN model(such as FCGN) and an IGN model. The behavior of a complete GN model isa desirable feature when determining if a route is safe to transmit dataonto (i.e., for path viability determination) since we would rather beslightly pessimistic in evaluating performance, but still very close tothe correct answer.

The results in FIGS. 4 and 5 could be achieved with a simplified GNmodel which has the implicit assumption of common fiber type on eachspan, so to show the true value of the FCGN model, FIG. 6 models themore realistic case of a random assortment of mixed fibers for which asimplified “complete” GN model could not be applied to. Here, a randomassortment of fibers is generated based on statistics from an actualnetwork on the likelihood of different common fiber types.

The fiber order in the model was as follows: [7×NDSF, 3×TWRS, 3×NDSF,3×Truewave Classic (TWC), 2× Enhanced Large Effective Area Fiber(ELEAF), 6×NDSF, 5×TWRS, 4×ELEAF, 2×TWC, 4×NDSF, 2×ELEAF, 3×TWC]. Theper-channel launch power for NDSF, TWRS, TWC, and ELEAF is 3 dBm, 0 dBm,0 dBm, and 1 dBm, respectively. In this heterogeneous fiber case, auniform baud rate systems and mixed baud rate systems are modeled. Theuniform baud system is modeled where all channels are 56 GBaud at 200Gb/s, while the mixed symbol rate system consists of 38 total 56 GBaud200 Gb/s channels and 38 total 35 GBaud 200 Gb/s channels, with 61.5 GHzand 37.5 GHz channel bandwidths for two symbol rates, respectively. Inboth cases, the probe channel at 1550 nm is a 56 GBaud, 200 Gb/schannel.

Looking at the results from FIG. 6, similar results are seen as FIGS. 4and 5, where the FCGN converges well with the conventional moduleresults and is always pessimistic if there is a discrepancy, whereas anincoherent model will start diverging and underestimating the nonlinearpenalty. This shows that the FCGN model would be an appropriate tool toestimate nonlinear penalty for rapid path viability determination evenin the realistic cases of heterogeneous fiber types and baud rates.

§ 4.2 Procedure for Path Viability Determination

The following procedure could be implemented on network element hardwaredirectly, or in an appropriate orchestration layer which may include acomputer or network of computers with north/south-bound communication tothe network element layer, or even in an offline modeling tool.

1) Starting at the add-node, first, perform the operation of findingpaths which have the appropriate contiguous frequency spectrum availableon an entire route from the add-node to the desired drop-node to supportthe required baud-rate of a given modern technology (which may beadapted in the case of variable baud-rate modems). The architecture ofthe Reconfigurable Optical Add/Drop Multiplexers (ROADMs) at theadd-node and drop-node, and which connected transceivers are availableand appropriately connected to client traffic will dictate whichdirections that can add and drop channels onto and whether it can handleMUX-path frequency contention. Once this is determined, the opticalfrequency spectrum (e.g., C-band, or C&L-bands) can be discretized intothe minimum resolution of Media Channels (MCs) which could be 6.25 GHz(e.g., 768 frequency slices for the C-band), where truth tables aregenerated for each optical section with a ‘1’ indicating that part ofthe frequency spectrum is occupied and a ‘0’ indicating the channelspace is available. On any given path from the add-node to drop-node(i.e., routing through any set of physically possible intermediatenodes), one can determine the parts of contiguous frequency spectrum bysimply running an OR operation across all truth-table vectors for eachoptical section within the path of interest and look for groups ofcontiguous 0's available indicating available spectrum.

2) Once it is known which sections are viable in terms of availablefrequency content, one would then model the physical impairments alongwith the set of paths under consideration which includes, but is notlimited to the following:

a) Determining power spectrum information at every node in the networkrequired for penalty modeling using a combination of simulated andmeasured data. This is done by forward modeling transfer functions ofdifferent line elements (e.g., Wavelength Dependent Loss (WDL) andStimulated Raman Scattering (SRS) in fiber, and the gain transferfunction in Erbium-Doped Fiber Amplifiers (EDFAs) due to homogeneous andinhomogeneous broadening, plus any lumped losses or filter shapes due)followed by a backward error correction when spectral information isavailable.

b) Modeling linear optical NSR impairments as a function of frequencyand section due to additive ASE generated from EDFAs and Ramanamplifiers. These impairments could either be modeled in real-time ormodeled once at system start-up (once system configuration includinglosses, gain settings, etc. are known) and stored for future access.

c) Modeling Tx/Rx impairment losses as well as eye-closure based eitheron data stored on the Tx/Rx pair, or table values, or a combination ofthe two.

d) Modeling Polarization Dependent Loss (PDL) penalty and filter penaltybased on the hardware on any given path and table values.

e) Modeling nonlinear coherent noise penalty based on the FCGN discussedabove.

f) If available, compare modeled results with other existing channelsthat can report effective SNR on the proposed path to determine howpessimistic the model is (e.g., compare against results from otherapproaches) and then modify estimated values to give a better gauge ofanticipated performance.

The performance of a path is then given by the effective delivered SNR,which includes the summation of all incremental NSR penalties due to thevarious effects along the path.

3) Once physical performance for every path is known (in terms of totaldelivered effective SNR), one would then compare the required SNR forthe available modems at the line-rates which are available to theestimated delivered SNR on each path to determine which paths are viablefor the required line-rates. Once this is known, some other path-rankingalgorithm could take over to decide the “best” path based on customerpreference (e.g., latency, minimum margin, maximum margin, etc.).

§ 4.3 SNR Performance

Optical path viability can be expressed as incremental SNR which is thepenalty due to an element (or set of elements) and which is given inlinear units as ΔSNR=(SNR_(out) ⁻¹−SNR_(in) ⁻¹)⁻¹, or more simplyconsidering noise to signal ratios (inverse SNR):ΔNSR=NSR_(out)−NSR_(in). Incremental SNR is the amount of the noise thatis contributed to the total SNR from the item under scrutiny, that itembeing a span, section, sub-path, or path. Using incremental NSR makesthe impact a direct proportionality to the margin. To determine thepenalty of a concatenation of elements, it is possible to sum theirincremental NSRs (by definition), namely NSR_(total)=ΣNSR_(i). In anembodiment, the term “span” refers to a span/amp combos considering boththe linear and nonlinear penalty contributions, which can beparameterized by fiber type, amplifier settings, fiber loss, as well assome other variables.

It is possible to view the NSR of each sub-component (item) of the totalwith respect to one another. Assume the NSR is expressed in dBs—One maychoose different colors or other visualizations to express link averageNSR. For example, at −15 dB, green may represent the link average NSR ofthe contributing elements. Elements that contribute more noise areyellow, and ones that contribute less are blue, etc.

However, understanding deltas in these variables alone does not give anyintuition into how much penalty is being imparted on the network.Rather, this is where exposing the incremental SNR (or equivalently NSR)penalty has clear, tangible value. Under nearly GN NLI cases, thephotonic performance delivered by the system can be presented withoutmodems (i.e., the delivered SNR of the system is not a property of thesignal, but the visualization decouples the intrinsic photonic systemperformance and reporting that which is very nearly modern agnostic).SNR is directly convertible to a theoretical capacity via theShannon-Hartley theorem (in fact, nearly linear relationship between SNRin dB and capacity in Gbps under many practical SNR regimes).

The present disclosure is also not focused only on the linearperformance, which is the OSA measurable OSNR or ASE. It is only whenyou include the actual signal power that the non-linear performance canbe calculated. When added to the linear performance, the totalincremental SNR is calculable. Of note, boiling the metric down to asingle parameter allows for visualization.

§ 4.4 Span Contribution

There are many possibilities related to how to report the perspan/section data (e.g., as absolute penalties, the penalty per unitdistance, relative to planned as you are highlighting, relative toplanned with some normalization, etc.), including in the context of apath.

For example, assume a 10-span optical system (e.g., two ROADM nodes withnine intermediate line amplifiers, i.e., ten links 120). Assume eachspan will contribute ˜ 1/10 of total noise. So, if one span is 3 dBworse, the total system will just look like an 11-span system, i.e., arelatively small degradation. However, the goal in the operation of theoptical network is to exploit unused margin, to mine such margin forextra capacity. So, in this case, with equal span penalties, a 3-dBdegradation in one span translates to a 0.4 dB total path penalty, whichmay push a channel from operating at a healthy margin to being close tothe edge or at failure.

In general, it is not true that on a randomly selected ten span path,one would expect equal penalty on each span and this is a point tohighlight (especially when showing per span penalty in absolute units)since there is a large distribution of fiber types, fiber losses, amptypes (with different Noise Figures (NF) in different gain ranges),OADMs with different penalties, etc. especially on networks built overtime or with uneven site spacing due to sensible geographical add/droplocations. It may be the case that in a ten span system, there is onespan contributing half of the total penalty, so when it's incrementalSNR penalty moves by 2 dB, it is actually shifting the total penalty ofthe path by 1.1 dB, and the penalty can be reported in the context ofthe path it's on (i.e., this 2 dB drop is contributing a degradation of1.1 dB of the total path SNR, whereas some other 2 dB drop on one of the“good” spans is degrading the total path SNR by 0.1 dB). There are alsoplenty of cases where there are a few spans, especially with higher ratemodems where the operation is close to the edge. In these cases, achange in one span may be even more significant.

These issues can lead to silent failures when a service tries to restoreonto them. As mentioned, many routes include a small number of hops. Asa part of capacity mining, a network operator is intentionally pushingthe modern rate to its minimum delivered margin on some routes whilebacking off to lower rates on routes that otherwise would not providesufficient margin.

This is precisely why these visualizations are useful. Fiber spans in areal network often have a large range of losses. FIG. 7 is a graph ofthe distribution of span losses in typical networks. Typical networkshave a log-normal distribution of span losses, as illustrated in FIG. 7.The difference between a 3 dB delta on a 10 dB span versus a 25 dB spanis significant; therefore, just looking at deltas is very misleading.The 10 dB span is insignificant comparatively, and using the NSR scalemakes that visually obvious.

§ 5.0 Heterogenous GN Derivation and Simplification

In this section, the coherent contribution from Self-ChannelInterference (SCI) is derived. The coherent term can be added to theexisting incoherent model. The following assumptions are made.

Lumped amplification is applied;

Only the coherent contribution of the probe to probe is considered (thecoherent contribution of interfering channel to probe is relativelysmall and can be ignored here);

Some assumptions would be followed in the derivation process; and

Higher-order dispersion coefficient is ignored.

The following parameters are used herein:

P_(n) _(s) power of probe channel at the beginning of n_(s) ^(th) span.specifically, P_(n) _(s) (m) is power for n_(s) ^(th) span for channel mP′_(n) _(s) power at the end of n_(s) ^(th) span. γ_(n) _(s) nonlinearcoefficient of n_(s) ^(th) span α_(n) _(s) optical power attenuationcoefficient of n_(s) ^(th) span. Optical power attenuates as exp (−α_(n)_(s) z). β_(2, n) _(s) second order dispersion of n_(s) ^(th) spanL_(s, n) _(s) span length for n_(s) ^(th) span L_(eff, n) _(s) effectivelength for n_(s) ^(th) span B_(ch) probe channel bandwidth

According to Eq. (100) of Poggiolini, Pierluigi, et al. “A detailedanalytical derivation of the GN model of non-linear interference incoherent optical transmission systems.” arXiv preprint arXiv:1209.0394(2012), the nonlinear power spectrum density from SCI for total N_(s)spans for central channel is (derivation is in § 5.1).

$\begin{matrix}{{G(f)} = {\frac{16}{27}{\int{\int_{- \infty}^{\infty}{{g( f_{1} )}{g( f_{2} )}{g( {f_{1} + f_{2} - f} )}{H_{N_{s}}( {f_{1},f_{2},f} )}{df}_{1}{df}_{2}}}}}} & (5.1) \\{{H_{N_{s}}( {f_{1},f_{2},f} )} = {{\sum\limits_{n_{s} = 1}^{N_{s}}{\gamma_{n_{s}}P_{n_{s}}P_{N_{s}}^{\prime\frac{1}{2}}{\exp\lbrack {j\;{\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack} \times {\xi_{n_{s}}( {f_{1},f_{2},f} )}}}}^{2}} & (5.2) \\{\mspace{79mu}{{\phi_{n_{s}}( {f_{1},f_{2},f} )} = {4{\pi^{2}( {f_{1} - f} )}( {f_{2} - f} ){\sum\limits_{n_{s}^{\prime} = 1}^{n_{s} - 1}{\beta_{2,n_{s}^{\prime}}L_{s,n_{s}^{\prime}}}}}}} & (5.3) \\{{\xi_{n_{s}}( {f_{1},f_{2},f} )} = \frac{1 - {{\exp( {{- \alpha_{n_{s}}}L_{s,n_{s}}} )}{\exp( {j\; 4\;{\pi^{2}( {f_{1} - f} )}( {f_{2} - f} )\beta_{2,n_{s}}L_{s,n_{s}}} )}}}{\alpha_{n_{s}} - {j\; 4{\pi^{2}( {f_{1} - f} )}( {f_{2} - f} )\beta_{2,n_{s}}}}} & (5.4)\end{matrix}$

where ϕ_(n) _(s) (f₁,f₂,f) is accumulated walk-off effect from thebeginning of link to the beginning of n^(th) span. In particular,ϕ₁(f₁,f₂,f)=0. g(f) is the normalized PSD for probe channel. ξ_(n) _(s)(f₁, f₂, f) is four-wave-mixing efficient for each span.

H_(N) _(s) (f₁, f₂, f) in Eq. 5.2 can be written as:

$\begin{matrix}{{H_{N_{s}}( {f_{1},f_{2},f} )} = {( {\sum\limits_{n_{s} = 1}^{N_{s}}{\gamma_{n_{s}}P_{n_{s}}P_{N_{s}}^{\prime\frac{1}{2}}{\exp\lbrack {j\;{\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack} \times {\xi_{n_{s}}( {f_{1},f_{2},f} )}}} )( {\sum\limits_{n_{s} = 1}^{N_{s}}{\gamma_{n_{s}}P_{n_{s}}P_{N_{s}}^{\prime\frac{1}{2}}{\exp\lbrack {j\;{\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack} \times {\xi_{n_{s}}( {f_{1},f_{2},f} )}}} )^{*}}} & (5.5)\end{matrix}$

Thus, the contribution for N_(s) ^(th) span can be expressed as:

$\begin{matrix}{{\Delta\;{H( {f_{1},f_{2},f} )}} = {{{H_{N_{s}}( {f_{1},f_{2},f} )} - {H_{N_{s} - 1}( {f_{1},f_{2},f} )}} = {{{{A_{N_{S}}( {f_{1},f_{2},f} )}{\exp\lbrack {j\;{\phi_{N_{s}}( {f_{1},f_{2},f} )}} \rbrack}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}{{A_{n_{s}}^{*}( {f_{1},f_{2},f} )}{\exp\lbrack {{- j}\;{\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}}}} + {{A_{N_{s}}^{*}( {f_{1},f_{2},f} )}{\exp\lbrack {{- j}\;{\phi_{N_{s}}( {f_{1},f_{2},f} )}} \rbrack}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}{{A_{n_{s}}( {f_{1},f_{2},f} )}{\exp\lbrack {j\;{\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}}}} + {{A_{N_{s}}( {f_{1} + f_{2} - f} )}}^{2}} = {{2{{A_{N_{s}}( {f_{1},f_{2},f} )}}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}{{{A_{n_{s}}( {f_{1},f_{2},f} )}}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )} + \theta_{N_{s}} - \theta_{n_{s}}} \rbrack}}}} + {{A_{N_{s}}( {f_{1},f_{2},f} )}}^{2}}}}} & (5.6) \\{\mspace{79mu}{{A_{n_{s}}( {f_{1},f_{2},f} )} = {\gamma_{n_{s}}P_{n_{s}}P_{N_{s}}^{\prime\frac{1}{2}}{\xi_{n_{s}}( {f_{1},f_{2},f} )}}}} & (5.7)\end{matrix}$

where θ_(n) _(s) is angle of A_(n) _(s) (f₁, f₂, f). When the ChromaticDispersion (CD) is large enough,

$\theta_{n_{s}} \approx \theta_{N_{s}} \approx {- \frac{\pi}{2}}$

Then

$\begin{matrix}{{\Delta\;{H( {f_{1},f_{2},f} )}} = {{2{{A_{N_{s}}( {f_{1},f_{2},f} )}}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}{{{A_{n_{s}}( {f_{1},f_{2},f} )}}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}}}} + {{A_{N_{s}}( {f_{1} + f_{2} - f} )}}^{2}}} & (5.8)\end{matrix}$

where the first term is the coherent contribution and second term is theSCI incoherent contribution of N_(s) ^(th) span. Put Eq. (5.8) into theEq. (5.1), the coherent contribution of N_(s) ^(th) span is as followed:

$\begin{matrix}{{G_{N_{s}}^{cc}(f)} = {{\frac{32}{27}{\int{\int_{- \infty}^{\infty}{{g( f_{1} )}{g( f_{2} )}{g( {f_{1} + f_{2} - f} )}{A_{N_{s}}( {f_{1},f_{2},f} )}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}{{{A_{n_{s}}( {f_{1},f_{2},f} )}}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}{df}_{1}{df}_{2}}}}}}} \approx {\sum\limits_{n_{s} = 1}^{N_{s} - 1}\sqrt{{B_{n_{s},N_{s}}(f)}{C_{n_{s},N_{s}}(f)}}}}} & (5.9) \\{{B_{n_{s},N_{s}}(f)} = {\frac{32}{27}{\int{\int_{- \infty}^{\infty}{{g( f_{1} )}{g( f_{2} )}{g( {f_{1} + f_{2} - f} )}{{A_{n_{s}}( {f_{1},f_{2},f} )}}^{2}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}{df}_{1}{df}_{2}}}}}} & (5.10) \\{{C_{n_{s},N_{s}}(f)} = {\frac{32}{27}{\int{\int_{- \infty}^{\infty}{{g( f_{1} )}{g( f_{2} )}{g( {f_{1} + f_{2} - f} )}{{A_{n_{s}}( {f_{1},f_{2},f} )}}^{2}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}{df}_{1}{df}_{2}}}}}} & (5.11)\end{matrix}$

If the signal spectrum is assumed to be rectangular, g(f)=1/B_(ch).Following the FWM efficiency assumption as Eq. (36), Appendix F inPoggiolini, Pierluigi. “The GN model of non-linear propagation inuncompensated coherent optical systems.” Journal of Lightwave Technology30.24 (2012): 3857-3879,

$\begin{matrix}{{B_{n_{s},N_{s}}(f)} = {\frac{32}{27}\frac{\gamma_{n_{s}}^{2}P_{n_{s}}^{2}P_{N_{s}}^{\prime}L_{{eff},n_{s}}^{2}}{B_{ch}^{3}}{\int{\int_{- \infty}^{\infty}{\frac{1}{1 + {16\;\pi^{4}\beta_{2,n_{s}}^{2}f_{1}^{2}{f_{2}^{2}/\alpha_{n_{s}}^{2}}}}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}{df}_{1}{df}_{2}}}}}} & (5.12) \\{{C_{n_{s},N_{s}}(f)} = {\frac{32}{27}\frac{\gamma_{N_{s}}^{2}P_{N_{s}}^{2}P_{N_{s}}^{\prime}L_{{eff},N_{s}}^{2}}{B_{ch}^{3}}{\int{\int_{- \infty}^{\infty}{\frac{1}{1 + {16\;\pi^{4}\beta_{2,N_{s}}^{2}f_{1}^{2}{f_{2}^{2}/\alpha_{N_{s}}^{2}}}}{\cos\lbrack {{\phi_{N_{s}}( {f_{1},f_{2},f} )} - {\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}{df}_{1}{df}_{2}}}}}} & (5.13)\end{matrix}$

Following a similar derivation method of Poggiolini, Pierluigi. “The GNmodel of non-linear propagation in uncompensated coherent opticalsystems.” Journal of Lightwave Technology 30.24 (2012): 3857-3879,appendix H, one obtains

$\begin{matrix}{{B_{N_{s}}(0)} \approx {\frac{16}{27}\frac{\gamma_{n_{s}}^{2}L_{{eff},n_{s}}^{2}P_{n_{s}}^{2}P_{N_{s}}^{\prime}}{\pi\;\tau_{{CD},n_{s}}B_{ch}^{3}}}} & (5.14) \\{{C_{N_{s}}(0)} \approx {\frac{16}{27}\frac{\gamma_{N_{s}}^{2}L_{{eff},N_{s}}^{2}P_{N_{s}}^{2}P_{N_{s}}^{\prime}}{\pi\;\tau_{{CD},n_{s}}B_{ch}^{3}}}} & (5.15)\end{matrix}$

where τ_(CD,n) _(s) =Σ_(k=n) _(s) ^(N) ^(s) ⁻¹β_(2,k)L_(s,k) is theaccumulated CD difference between N_(s) ^(th) span and n_(s) ^(th) span.As a result, coherent contribution of N_(s) ^(th) span is as follows

$\begin{matrix}{{G_{N_{s}}^{cc}(0)} = {\frac{16}{27}\frac{P_{N_{s}}^{\prime}\gamma_{N_{s}}L_{{eff},N_{s}}P_{N_{s}}}{\pi\; B_{ch}^{3}}P_{N_{s}}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}\frac{\gamma_{n_{s}}L_{{eff},n_{s}}P_{n_{s}}}{\tau_{{CD},n_{s}}}}}} & (5.16)\end{matrix}$

The coherent NSR for N^(th) span only is

$\begin{matrix}{{NSR}_{{NL},N}^{cc} = {\frac{16}{27}\frac{\gamma_{N_{s}}L_{{eff},N_{s}}P_{N_{s}}}{\pi\; B_{ch}^{2}}{\sum\limits_{n_{s} = 1}^{N_{s} - 1}\frac{\gamma_{n_{s}}L_{{eff},n_{s}}P_{n_{s}}}{\tau_{{CD},n_{s}}}}}} & (5.17)\end{matrix}$

§ 5.1 Appendix—Heterogenous GN Derivation and Simplification

The PSD at the beginning of n_(s) ^(th) span is

G _(sig,n) _(s) (f)=P _(n) _(s) (1)g(f,1)+P _(n) _(s) (2)g(f,2)+ . . .+P _(n) _(s) (N _(ch))g(f,N _(ch))  (5.A.1)

The corresponding amplitude of electric field is

√{square root over (G _(sig,n) _(s) (f))}=√{square root over (P _(n)_(s) (1)g(f,1))}+√{square root over (P _(n) _(s) (2)g(f,2))}+ . . .+√{square root over (P _(n) _(s) (N _(ch))g(f,N _(ch)))}  (5.A.2)

Where P_(n) _(s) (m) is the power for channel m at the beginning ofn_(s). And one has ∫_(−∞) ^(∞)g(f,m)=1 for the normalized PSD for m^(th)channel. We have g(f,m)g(f,n)=0 if m≠n.

Consequently, if ignoring the double integration, FWM term, summationover span and square operator, and only considering applying the firstproduct of sequence in Eq. (100), from Poggiolini, Pierluigi, et al. “Adetailed analytical derivation of the GN model of non-linearinterference in coherent optical transmission systems.” arXiv preprintarXiv:1209.0394 (2012), to obtain

$\begin{matrix}{{E_{n_{s}}(f)} = {{\prod\limits_{n_{s}^{\prime} = 1}^{n_{s} - 1}\sqrt{{G_{Tx}( f_{1} )}{G_{Tx}( f_{2} )}{G_{Tx}( {f_{1} + f_{2} - f} )}\Gamma_{n_{s}^{\prime}}^{3}{\exp( {{- 3}\;\alpha_{n_{s}^{\prime}}L_{n_{s}^{\prime}}} )}}} = {{\prod\limits_{n_{s}^{\prime} = 1}^{n_{s} - 1}{\sqrt{{G_{Tx}( f_{1} )}\Gamma_{n_{s}^{\prime}}{\exp( {{- \alpha_{n_{s}^{\prime}}}L_{n_{s}^{\prime}}} )}}\sqrt{{G_{Tx}( f_{2} )}{\exp( {{- \alpha_{n_{s}^{\prime}}}L_{n_{s}^{\prime}}} )}}\sqrt{{G_{Tx}( {f_{1} + f_{2} - f} )}\Gamma_{n_{s}^{\prime}}{\exp( {{- \alpha_{n_{s}^{\prime}}}L_{n_{s}^{\prime}}} )}}}} = {{\sqrt{G_{{sig},n_{s}}( f_{1} )}\sqrt{G_{{sig},n_{s}}( f_{2^{\prime}} )}\sqrt{G_{{sig},n_{s}}( {f_{1} + f_{2} - f} )}} = {\sum\limits_{m_{1} = 1}^{N_{ch}}{\sqrt{{P_{n_{s}}( m_{1} )}{g( {f_{1},m_{1}} )}}{\sum\limits_{m_{2} = 1}^{N_{ch}}{\sqrt{{P_{n_{s}}( m_{2} )}{g( {f_{1},m_{2}} )}}{\sum\limits_{m_{3} = 1}^{N_{ch}}\sqrt{{P_{n_{s}}( m_{3} )}{g( {f_{1},m_{3}} )}}}}}}}}}}} & ( {5.A{.3}} )\end{matrix}$

where Γ_(n) _(s) _(′) is the gain of n′_(s) span.

The above expression is the beating term from three pumps. In thiscoherent model, only consider the coherent contribution from probechannel, which means only the coherent contribution of self-channelinterference (SCI) is considered, Eq. (5.A. 3) can be simplified as

$\begin{matrix}{{{E( {f,n_{s}} )} \approx {\sum\limits_{m = 1}^{N_{ch}}{\sqrt{{P_{n_{s}}(m)}{g( {f_{1},m} )}}\sqrt{{P_{n_{s}}(m)}{g( {f_{2},m} )}}\sqrt{{P_{n_{s}}(m)}{g( {{f_{1} + f_{2} - f},m} )}}}}} = {\sum\limits_{m = 1}^{N_{ch}}{{P_{n_{s}}(m)}^{3/2}\sqrt{g( {f_{1},m} )}\sqrt{g( {f_{2},m} )}\sqrt{g( {{f_{1} + f_{2} - f},m} )}}}} & ( {5.A{.4}} )\end{matrix}$

Applying the second product of sequence in Eq. (100), Poggiolini,Pierluigi, et al. “A detailed analytical derivation of the GN model ofnon-linear interference in coherent optical transmission systems.” arXivpreprint arXiv:1209.0394 (2012).

$\begin{matrix}{{( {f,n_{s}} ){\prod\limits_{n_{s}^{\prime} = n_{s}}^{N_{s}}{\Gamma_{n_{s}^{\prime}}^{\frac{1}{2}}{\exp( {- \frac{\alpha_{n_{s}^{\prime}}L_{n_{s}^{\prime}}}{2}} )}}}} = {{\sum\limits_{m = 1}^{N_{ch}}{{P_{n_{s}}(m)}^{\frac{3}{2}}\sqrt{g( {f_{1},m} )}\sqrt{g( {f_{2},m} )}\sqrt{g( {{f_{1} + f_{2} - f},m} )}{\prod\limits_{n_{s}^{\prime} = n_{s}}^{N_{s}}{\Gamma_{n_{s}^{\prime}}^{\frac{1}{2}}{\exp( {- \frac{\alpha_{n_{s}^{\prime}}L_{n_{s}^{\prime}}}{2}} )}}}}} = {{\sum\limits_{m = 1}^{N_{ch}}{{P_{n_{s}}(m)}^{\frac{3}{2}}\frac{{P_{N_{s}}^{\frac{1}{2}}(m)}\Gamma_{N_{s}}^{\frac{1}{2}}{\exp( {- \frac{\alpha_{N_{s}}L_{N_{s}}}{2}} )}}{{P_{n_{s}}(m)}^{\frac{1}{2}}}\sqrt{g( {f_{1},m} )}\sqrt{g( {f_{2},m} )}\sqrt{g( {{f_{1} + f_{2} - f},m} )}}} = {\sum\limits_{m = 1}^{N_{ch}}{{P_{n_{s}}(m)}{P_{N_{s}}^{1/2}(m)}\Gamma_{N_{s}}^{\frac{1}{2}}{\exp( {{- \alpha_{N_{s}}}{L_{N_{s}}/2}} )}\;\sqrt{g( {f_{1},m} )}\sqrt{g( {f_{2},m} )}\sqrt{g( {{f_{1} + f_{2} - f},m} )}}}}}} & ( {5.A{.5}} )\end{matrix}$

As a result, if we only consider the nonlinearity for a certain probechannel and remove the channel index,

$\begin{matrix}{{G(f)} = {\frac{16}{27}{\int{\int_{- \infty}^{\infty}{{g( f_{1} )}{g( f_{2} )}{g( {f_{1} + f_{2} - f} )}{H_{N}( {f_{1},f_{2},f} )}{df}_{1}{df}_{2}}}}}} & ( {5.A{.6}} ) \\{{H_{N_{s}}( {f_{1},f_{2},f} )} = {{\sum\limits_{n_{s} = 1}^{N}{\gamma_{n_{s}}P_{n_{s}}P_{N_{s}}^{\prime\frac{1}{2}}{\exp\lbrack {j\;{\phi_{n_{s}}( {f_{1},f_{2},f} )}} \rbrack}*{\xi_{n_{s}}( {f_{1},f_{2},f} )}}}}^{2}} & ( {5.A{.7}} ) \\{\mspace{79mu}{P_{N_{s}}^{\prime\frac{1}{2}} = {P_{N_{s}}^{\frac{1}{2}}\Gamma_{N_{s}}^{\frac{1}{2}}{\exp( {{- \alpha_{N_{s}}}{L_{N_{s}}/2}} )}}}} & ( {5.A{.8}} ) \\{\mspace{79mu}{{\phi_{n_{s}}( {f_{1},f_{2},f} )} = {4\;{\pi^{2}( {f_{1} - f} )}( {f_{2} - f} ){\sum\limits_{n_{s}^{\prime} = 1}^{n_{s} - 1}{\beta_{2,n_{s^{\prime}}}L_{s,n_{s^{\prime}}}}}}}} & ( {5.A{.9}} ) \\{{\xi_{n_{s}}( {f_{1},f_{2},f} )} = \frac{1 - {{\exp( {{- \alpha_{n_{s}}}L_{s,n_{s}}} )}{\exp( {j\; 4\;{\pi^{2}( {f_{1} - f} )}( {f_{2} - f} )\beta_{2,n_{s}}L_{s,n_{s}}} )}}}{\alpha_{n_{s}} - {j\; 4\;{\pi^{2}( {f_{1} - f} )}( {f_{2} - f} )\beta_{2,n_{s}}}}} & ( {5.A{.10}} )\end{matrix}$

Where g(f) is the normalized PSD for the probe channel.

§ 6.0 Proposed Incoherent GN Model and Results

In an embodiment, the NLI power spectral density (PSD) at a frequency,f, is calculated using an incoherent GN (IGN) model as follows inequations (6.1)-(6.2):

$\begin{matrix}{{G(f)} = {\frac{16}{27}{\sum\limits_{k = 1}^{N_{s}}{\int_{- \infty}^{\infty}\;{\int_{- \infty}^{\infty}{\gamma_{k}^{2}{G_{{WDM},k}( f_{1} )}{G_{{WDM},k}( f_{2} )}{G_{{WDM},k}( {f_{1} + f_{2} - f} )}{\frac{1 - {e^{{- 2}\;\alpha_{k}L_{s,k}}e^{j\; 4\;\beta_{2,k}{L_{s,k}{({f_{1} - f})}}{({f_{2} - f})}}}}{{2\;\alpha_{k}} - {j\; 4\;\pi^{2}{\beta_{2,k}( {f_{1} - f} )}( {f_{2} - f} )}}}^{2}{df}_{1}{df}_{2}}}}}}} & (6.1)\end{matrix}$

where, N_(s) is the number of total spans. β_(2,k), γ_(k), α_(k) andL_(s,k) are the second-order dispersion coefficient, nonlinearcoefficient, field attenuation coefficient and span length for k^(th)span respectively, and G_(WDM,k) is the signal PSD in the k^(th) span.

In typical WDM systems, Self-Channel Interference (SCI) and Cross-PhaseModulation (XPM) are the dominant NLI contributions, see Carena A, BoscoG, Curri V, et al.: ‘EGN model of non-linear fiber propagation,’ OpticsExpress, 2014, 22, (13), pp. 16335-62. As a result, the proposed IGN QMCmodel only takes SCI and XPM into consideration. If one takes the signaland nonlinear noise to be flat over the bandwidth of the channel, thenonlinear NSR in a single span for probe channel n at frequency f isexpressed simply as:

$\begin{matrix}{{NSR}_{{NL},n} = {\frac{16}{27}g_{m}{\sum\limits_{m = 1}^{N_{ch}}{P_{m}^{2}\phi_{m,n}}}}} & ( {6.2a} ) \\{\phi_{m,n} = {\frac{\gamma_{m}^{2}}{B_{{ch},m}}\frac{B_{{ch},n}}{N_{samp}}{\sum\limits_{k = 1}^{Nsamp}{\frac{1 - {e^{{- \alpha_{m}}L_{s}}e^{j\; 4\;\pi^{2}\beta_{2,m}L_{s}{f_{1}{(k)}}{f_{2}{(k)}}}}}{\alpha_{m} - {j\; 4\;\pi^{2}\beta_{2,m}{f_{1}(k)}{f_{2}(k)}}}}^{2}}}} & ( {6.2b} ) \\{{{{f_{1}(k)} + {f_{2}(k)} - ( {f_{m} - f_{n}} )}} \leq {B_{{ch},m}/2}} & ( {6.2c} )\end{matrix}$

where ϕ_(m,n) is the normalized NLI coefficient, n and m are probechannel and interfering channel, respectively, g_(m)=2 if m≠n andg_(m)=1 if m=n, N_(ch) is the total number of channels, B_(ch,m), P_(m)and f_(m) are bandwidth, launch power and central frequency respectivelyfor channel m, N_(samp) is the number of samples for Quasi-Monte Carlomethod, and (f₁(k),f₂(k)) is a pair of low-discrepancy random sequences.

An important feature of Equations (6.2) is the separation of the fibercharacteristics and power spectrum into the fiber. In many cases, thefiber characteristics on a modeled system do not change, such thatϕ_(m,n) need only be evaluated once for a given channel plan. This meansthe NLI can be evaluated very efficiently on the same fiber or set offibers with many different launch power profiles using Eq. (6.2a).

The IGN QMC has the same benefits as other IGN model variants, where thecontributions from all interfering channels are individually consideredon a per span basis. This allows the model to operate on dynamicnetworks with different channel layouts on different spans, and onheterogeneous links where the fibers in the path have varyingproperties. The critical difference of the IGN QMC proposed comparedwith approximate analytic solutions of the IGN model is that it makesfewer assumptions and is thus valid in low span loss regimes, which arecommon in commercially deployed networks.

Some previous work has shown the application of the standard Monte Carlomethod to solve the double integral in the GN model, see Dar R, Feder M,Mecozzi A, et al. Accumulation of nonlinear interference noise infiber-optic systems, Optics Express, 2014, 22, (12), pp. 14199-211. Inthe standard Monte Carlo method, (f₁(k),f₂(k)) would be a pair selectedfrom a random sequence. The following section compares the standardMonte Carlo integration in the IGN model (IGN MC) with the proposed IGNQMC.

§ 6.1 Results

For span length impact, a single-span simulation is used to investigatethe impact of span length on the models, as shown in FIGS. 8(a) and 8(b)which are graphs of Nonlinear NSR for NDSF (FIG. 8(a)) and TWC (FIG.8(b)) under different span lengths. The simulation is of a 9-channel WDMsystem where each signal is ASE shaped to mimic a 56.8 GBaudtransponder. The probe is the central signal located at 1550 nm, and thechannel spacing is 75 GHz. The total power in each signal modeled is 3dBm for non-dispersion shifted fiber (NDSF) and 1 dBm for TrueWaveclassic (TWC) fiber. The dispersion coefficient, attenuation, andeffective area all specified at 1550 nm are 16.8 ps·nm⁻¹ km⁻¹, 0.2 dB/kmand 79.6 um⁻² for NDSF, respectively, and 2.8 ps·nm⁻¹ km⁻¹, 0.21 dB/kmand 51.7 um⁻² for TWC, respectively. Dispersion slope is included usinga frequency-dependent β₂ in Equation (6-2b). The IGN CF line is theclosed-form IGN model of Eq. (40) in Poggiolini P.: ‘The GN model ofnon-linear propagation in uncompensated coherent optical systems.’Journal of Lightwave Technology, 2012, 30, (24), pp 3857-79, the SSFMline is the split-step Fourier method, and the IGN QMC line is theproposed IGN model.

As shown in FIGS. 8(a) and 8(b), IGN QMC matches well with the SSFM forthe ASE signal, while IGN CF has poor performance at shorter spanlength. The deviation of IGN CF compared to SSFM is around 5 dB for NDSFat 10 km. This discrepancy is expected since the IGN CF is based on anassumption of higher span loss, which results in the inaccuracy at lowerspan loss. Since IGN QMC accurately solves the GN reference model doubleintegral, the result of IGN QMC is very similar to an SSFM propagatingASE signals over a single span.

As described herein, there have been reports of Monte Carlo (MC) methodsbeing used to solve the integration in the GN model. FIGS. 9(a)-9(c) aregraphs of the convergence rate of IGN MC and IGN QMC for NDSF with 30 km(FIG. 9(a)), NDSF with 80 km (FIG. 9(b)), and TWC with 80 km (FIG.9(c)). FIGS. 9(a)-9(c) compare the convergence rate of the IGN MC andthe IGN QMC for (a) 30 km of NDSF, (b) 80 km of NDSF, and (c) 80 km ofTWC. The simulation is a full C-band WDM system with 64 channels on a 75GHz channel spacing, where each signal has a width commensurate with56.8 GBaud transmissions. The probe signal is the central one located at1547.8 nm. As shown in FIGS. 9(a)-9(c), IGN QMC can achieve convergencemuch faster than IGN MC. The required number of samples (RNS) for eachmethod to achieve convergence is shown in the following Table 1.Convergence is deemed to be achieved when the nonlinear NSR is within±0.15 dB of the accurate value.

TABLE 1 Required number of samples for both IGN methods Test case NDSF30 km NDSF 80 km TWC 80 km RNS of IGN QMC 2000 2000 100 RNS of IGN MC110000 45000 30000

This demonstrates that the RNS for IGN QMC is up to 300 times less thanthat of IGN MC. The total calculation time to evaluate the nonlinearityover a single span for all channels in the C-band using MATLAB is shownin Table 2. Note for the proposed IGN QMC, the required timing is thecalculation time of NLI the first time for a given span/channel plan. Ifthe link and the channel plan did not change, the required timing couldbe around 1000 times faster on the subsequent runs. It should be notedthat using the built-in integration functions such as trapz or integralin MATLAB requires on the order of minutes to evaluate the nonlinear NSRover C-band. The quasi-Monte Carlo approach shows an improvement ofgreater than three orders of magnitude even for spans of nominal length.The improvements are stronger for short spans as expected. From theseresults, one can conclude that the IGN QMC is a good candidate methodfor real-time nonlinear NSR estimation, especially when shorter spanlengths are present.

TABLE 2 Relative timing for both IGN methods over C band Test case NDSF30 km NDSF 80 km TWC 80 km IGN QMC 0.2 s 0.2 s 0.02 s IGN MC 8.2 s 3.4 s 2.3 s

Previous sections compared results for GN propagation as a proxy foractual modulated signals. To investigate the performance of IGN in areal system, a simulation was performed of a 21-channel WDM systemtransmission with 35 GBaud dual-polarization (DP)-16QAM signals. Theprobe channel is located at the central channel with a wavelength ofapproximately 1550 nm. FIGS. 10(a) and 10(b) are graphs of the Delta NSR(the difference between IGN and SSFM) with 16 QAM for NDSF (FIG. 10(a)and TWC (FIG. 10(b)). Delta nonlinear NSR is defined as the differencebetween IGN QMC (or IGN CF) and SSFM. The total signal powers at theinput to each span are 3 dBm for NDSF and 1 dBm for TWC, respectively.As shown in the graph of FIGS. 10(a) and 10(b), the error of IGN QMCcompared to SSFM is within 1 dB for all the cases investigated afterpropagating for ten spans. For IGN CF, when the span length is small,e.g., 10 km and 30 km, it suffers from a large amount of error comparedto SSFM. If the span length is increased to 90 km, the accuracy of IGNCF is comparable with IGN QMC.

Compared to the usual IGN model with a closed-form solution, theproposed approach is more accurate for short fibers. In addition, theQMC method shows significantly reduced computation times up to the orderof 100 times when compared to a standard Monte-Carlo approach.

§ 7.0 Process of Utilizing an Incremental Noise Metric for RapidModeling of Optical Networks

FIG. 11 is a flowchart of a process 50 of utilizing an incremental noisemetric for the rapid modeling of optical networks. The process 50contemplates implementation as a method, as computer readable codestored in a non-transitory computer-readable storage medium, and via aprocessing device. The process 50 includes receiving data for aplurality of elements associated with an optical network (step S11);determining an incremental noise penalty for each element of theplurality of elements based on the received data (step S12); and storingthe incremental noise penalty for each element of the plurality ofelements (step S13). The process 50 can further include determiningSignal-to-Noise Ratio (SNR) across an optical path in the opticalnetwork by concatenating associated incremental noise penalties for eachelement in the optical path along with corrections (step S14).

The corrections can be for upstream incremental noise penalties forelements upstream from the associated element, such as described in §§3.0-4.0. The SNR can be determined in real-time based on utilizingstored incremental noise penalties. The SNR for the optical path can beutilized as a cost metric in path computation. The process 50 canfurther include utilizing the SNR for the optical path to determine ifany of a pre-planned restoration route for an optical channel and a newroute for a new optical channel is currently viable. The process 50 canfurther include identifying sections in the optical network that needmaintenance or repair based on monitoring associated incremental noisepenalties. The process 50 can further include periodically performingthe obtaining, the determining, and the storing; and monitoring theassociated incremental noise penalties over time.

§ 7.1 Other Applications

The incremental noise penalties and SNR can be visually presented invarious format for example, reporting the information in plain text oranother encoded format which may be less usable to an end-user butuseful for higher level machine applications.

In an embodiment, the incremental noise penalties can be used in routingand path computation, such as “SNR-based routing”: Determining [new]paths which are viable (as opposed to determining viability of a givenpath) via performance based (SNR or NSR based) routing as opposed toexisting approaches which find a path based on other constraints andthen check viability. It is also possible to add the incremental SNRinto the cost function to ensure that the path found is viable duringRouting, Modulation, and Spectrum Assignment (RMSA).

Also, this can be used for noise localization—to determine whichdiscrete elements (amplifiers, spans) or concatenations of them(sections, or otherwise) of a network are giving noteworthy (e.g., high)penalty. This is of use to prioritize repair, maintenance, orreplacement of network infrastructure, debug network performance, changeroute prioritization for planned channels, variable bandwidthrestoration (find protect routes with different bandwidth values asworking routes), bandwidth optimization applications.

§ 8.0 Example Optical Network

FIG. 12 is a network diagram of a network 100 with five interconnectedsites 110 a, 110 b, 110 c, 110 d, 110 e. The sites 110 areinterconnected by a plurality of links 120, i.e., fiber. Each of thesites 110 can include a switch 122 and one or more WDM network elements124. The switch 122 is configured to provide services at Layers 1 (e.g.,Optical Transport Network (OTN)) and/or Layer 2 (e.g., Ethernet,Multiprotocol Label Switching (MPLS)) and/or Layer 3 (e.g., InternetProtocol (IP)) where the switch would normally be called a router. TheWDM network elements 124 provide the photonic layer (e.g., Layer 0) andvarious functionality associated therewith (e.g., multiplexing,amplification, optical routing, wavelength conversion/regeneration,local add/drop, etc.) including photonic control. Of note, while shownseparately, those of skill in the art will recognize that the switch 122and the WDM network elements 124 may be realized in the same networkelement. For example, a switch 122 can include pluggable transceiversthat provide WDM. The photonic layer and the photonic control operatingthereon can also include intermediate amplifiers and/or regenerators onthe links 120, which are omitted for illustration purposes. The network100 is illustrated, for example, as an interconnected mesh network, andthose of skill in the art will recognize the network 100 can includeother architectures, with additional sites 110 or with fewer sites, withadditional network elements and hardware, etc. The sites 110 communicatewith one another optically over the links 120, and the links 120 betweeneach of the sites 110 are examples of OMS, i.e., sections.

The network 100 includes a control plane 140 operating on and/or betweenthe switches 122 at the sites 110 a, 110 b, 110 c, 110 d, 110 e. Thecontrol plane 140 includes software, processes, algorithms, etc. thatcontrol configurable features of the network 100, such as automating thediscovery of the switches 122, the capacity of the links 120, portavailability on the switches 122, connectivity between ports;dissemination of topology and bandwidth information between the switches122; calculation and creation of paths for connections; network-levelprotection and restoration; and the like. Those of ordinary skill in theart will recognize the optical network 100, and the control plane 140can utilize any type of control plane for controlling the switches 122and establishing connections.

The optical network 100 can include photonic control 150, which can beviewed as a control algorithm/loop for managing wavelengths/opticalspectrum from a physical perspective at Layer 0. In one aspect, thephotonic control 150 is configured to add/remove wavelengths/spectrumfrom the links 120 in a controlled manner to minimize impacts toexisting, in-service wavelengths. For example, the photonic control 150can adjust modern launch powers, optical amplifier gain, VariableOptical Attenuator (VOA) settings, Wavelength Selective Switch (WSS)parameters, etc. The photonic control 150 can also be adapted to performnetwork optimization on the links 120. This optimization can alsoinclude re-optimization where appropriate. In an embodiment, thephotonic control 150 can adjust the modulation format, baud rate,frequency, wavelength, spectral width, etc. of optical modems inaddition to the aforementioned components at the photonic layer. In anembodiment, the photonic control 150 can include support for capacitymining where the physical parameters are adjusted to provide increasedcapacity without requiring additional hardware. For both the controlplane 140 and the photonic control 150, associated controllers can beeither centralized, distributed, or embedded in the network elements. Akey aspect of the optical network is the technology is fundamentallyanalog, and optical performance is subject to various linear andnon-linear impairments on the links 120.

The optical network 100 can also include a Software-Defined Networking(SDN) controller 160. SDN allows the management of network servicesthrough abstraction of lower-level functionality. This is done bydecoupling the system that makes decisions about where traffic is sent(SDN control through the SDN controller 160) from the underlying systemsthat forward traffic to the selected destination (i.e., the physicalequipment in the optical network 100). SDN calls for the ability tocentrally program provisioning of forwarding on the optical network 100for more flexible and precise control over network resources to supportnew services. The SDN controller 160 is a processing device that has aglobal view of the optical network 100. Additionally, the SDN controller160 can include or connect to SDN applications which can utilize thedata from the SDN controller 160 for various purposes.

A management system 170 can be a processing device that supportsOperations, Administration, Maintenance, and Provisioning (OAM&P)functions for the optical network 100. The management system 170 can bereferred to as a Network Management System (NMS), an Element ManagementSystem (EMS), a Craft Interface (CI), etc. The management system canconnect directly to the switches 122 and/or network elements 124, aswell as connect through any of the control plane 140, the photoniccontrol 150, the SDN controller 160, etc. The management system 170 canbe configured to provide a Graphical User Interfaces (GUI) forvisualizing networking functions, as described herein.

The control plane 140, the photonic control 150, the SDN controller 160,the management system 170, or some other server or processing device, aswell as a combination thereof, is configured to perform path computationand creation for connections; network-level protection and restoration;and the like. The rapid modeling described herein is advantageous in thecontext of network management, path computation, and the like.

Routing in the optical network 100 is well known. A path is consideredvalid for connection setup based on the availability of the switch 122,the links 120, sufficient bandwidth available thereon, and pathviability. Photonic networks, i.e., Layer 0 and the wavelengthinterconnectivity of the WDM network elements 124, introduce additionalcomplexity of successfully setting up a service. This can require thatall Layer 0 services are pre-planned and/or managed manually. Forexample, potential paths for services at the photonic layer can bepre-planned by modeling them offline using a static snapshot of thenetwork state to ensure that the computed paths are optically viable interms of reach, nonlinear effects, dispersion, wavelengthcontention/blocking, etc. Here, the engineering ensures that eachwavelength placed into service will work in a worst-case SNR.Alternatively, the paths can be computed at run-time. Of course, acombination is possible. The rapid modeling described herein isespecially useful in determining path viability at run-time as thisapproach is real-time.

FIG. 13 is a network diagram of another optical network illustratingadditional details of the photonic control 150, and the SDN controller160. The example of FIG. 12 illustrates a switch 122 that connects to aWDM network element 124, which connects to another WDM network element124 via a ROADM-to-ROADM section 180. The ROADM-to-ROADM section 180represents a portion of the network 100 between spectrum add/droppoints, e.g., ROADMs and can be referred to as the OMS. The photoniccontrol 150 can be an in-skin controller 190, which operates with theSDN controller 160. In-skin means the controller 190 is local with anetwork element, e.g., a pluggable module in a chassis.

FIG. 13 is a block diagram of a control environment that was used in afield trial and which is applicable to the methods and systems herein.The in-skin controller 190 retrieves the per-channel power measurements,Pi, of channels transiting the section 180 section (a section isall-optical). These per channel measurements are used to estimate theincremental Optical Signal-to-Noise Ratio (OSNR) for each channel,OSNRi. The in-skin controller 190 then attempts to equalize the OSNR ofeach channel to that of the average of all channels.

§ 9.0 Processing Device

FIG. 14 is a block diagram of a processing device 200, which may be usedto implement the SDN controller 160, the management system 170, thein-skin controller 190, a user device, etc. In the systems and methodsdescribed herein, the processing device 200 can be used to present aUser Interface (UI) or Graphical UI (GUI) to an operator forimplementing part of all of the various processes described herein. Theprocessing device 200 may be a digital computer that, in terms ofhardware architecture, generally includes a processor 202, input/output(I/O) interfaces 204, a network interface 206, a data store 208, andmemory 210. It should be appreciated by those of ordinary skill in theart that FIG. 14 depicts the processing device 200 in an oversimplifiedmanner, and practical embodiments may include additional components andsuitably configured processing logic to support known or conventionaloperating features that are not described in detail herein. Thecomponents (202, 204, 206, 208, and 210) are communicatively coupled viaa local interface 212. The local interface 212 may be, for example, butnot limited to, one or more buses or other wired or wirelessconnections, as is known in the art. The local interface 212 may haveadditional elements, which are omitted for simplicity, such ascontrollers, buffers (caches), drivers, repeaters, and receivers, amongmany others, to enable communications. Further, the local interface 212may include address, control, and/or data connections to enableappropriate communications among the aforementioned components.

The processor 202 is a hardware device for executing softwareinstructions. The processor 202 may be any custom made or commerciallyavailable processor, a central processing unit (CPU), an auxiliaryprocessor among several processors associated with the processing device200, a semiconductor-based microprocessor (in the form of a microchip orchipset), or generally any device for executing software instructions.When the processing device 200 is in operation, the processor 202 isconfigured to execute software stored within the memory 210, tocommunicate data to and from the memory 210, and to generally controloperations of the processing device 200 pursuant to the softwareinstructions. The I/O interfaces 204 may be used to receive user inputfrom and/or for providing system output to one or more devices orcomponents.

The network interface 206 may be used to enable the processing device200 to communicate over a network, such as the Internet, a wide areanetwork (WAN), a local area network (LAN), and the like, etc. Thenetwork interface 206 may include, for example, an Ethernet card oradapter or a wireless local area network (WLAN) card or adapter. Thenetwork interface 206 may include address, control, and/or dataconnections to enable appropriate communications on the network. A datastore 208 may be used to store data. The data store 208 may include anyof volatile memory elements (e.g., random access memory (RAM, such asDRAM, SRAM, SDRAM, and the like)), nonvolatile memory elements (e.g.,ROM, hard drive, tape, CDROM, and the like), and combinations thereof.Moreover, the data store 208 may incorporate electronic, magnetic,optical, and/or other types of storage media. In one example, the datastore 208 may be located internal to the processing device 200, such as,for example, an internal hard drive connected to the local interface 212in the processing device 200. Additionally, in another embodiment, thedata store 208 may be located external to the processing device 200,such as, for example, an external hard drive connected to the I/Ointerfaces 204 (e.g., SCSI or USB connection). In a further embodiment,the data store 208 may be connected to the processing device 200 througha network, such as, for example, a network-attached file server.

The memory 210 may include any of volatile memory elements (e.g., randomaccess memory (RAM, such as DRAM, SRAM, SDRAM, etc.)), nonvolatilememory elements (e.g., ROM, hard drive, tape, CDROM, etc.), andcombinations thereof. Moreover, the memory 210 may incorporateelectronic, magnetic, optical, and/or other types of storage media. Notethat the memory 210 may have a distributed architecture, where variouscomponents are situated remotely from one another but can be accessed bythe processor 202. The software in memory 210 may include one or moresoftware programs, each of which includes an ordered listing ofexecutable instructions for implementing logical functions. The softwarein the memory 210 includes a suitable operating system (O/S) 214 and oneor more programs 216. The operating system 214 essentially controls theexecution of other computer programs, such as the one or more programs216, and provides scheduling, input-output control, file and datamanagement, memory management, and communication control and relatedservices. The one or more programs 216 may be configured to implementthe various processes, algorithms, methods, techniques, etc. describedherein.

The processing device 200 can be connected to the OAM&P communicationnetwork in the network 100, such as via the network interface 206. Thisconnection provides a conduit through which the hardware in the network100 can be programmed following instructions from the SDN controller160, the control plane 140, and/or the photonic control 150. Theconnection further enables the processing device 200 to obtain data fromthe optical network 100 for use in the processes described herein.

Also, it will be appreciated that some embodiments described herein mayinclude one or more generic or specialized processors (“one or moreprocessors”) such as microprocessors; Central Processing Units (CPUs);Digital Signal Processors (DSPs): customized processors such as NetworkProcessors (NPs) or Network Processing Units (NPUs), Graphics ProcessingUnits (GPUs), or the like; Field Programmable Gate Arrays (FPGAs); andthe like along with unique stored program instructions (including bothsoftware and firmware) for control thereof to implement, in conjunctionwith certain non-processor circuits, some, most, or all of the functionsof the methods and/or systems described herein. Alternatively, some orall functions may be implemented by a state machine that has no storedprogram instructions, or in one or more Application-Specific IntegratedCircuits (ASICs), in which each function or some combinations of certainof the functions are implemented as custom logic or circuitry. Ofcourse, a combination of the aforementioned approaches may be used. Forsome of the embodiments described herein, a corresponding device inhardware and optionally with software, firmware, and a combinationthereof can be referred to as “circuitry configured or adapted to,”“logic configured or adapted to,” etc. perform a set of operations,steps, methods, processes, algorithms, functions, techniques, etc. ondigital and/or analog signals as described herein for the variousembodiments.

Moreover, some embodiments may include a non-transitorycomputer-readable storage medium having computer readable code storedthereon for programming a computer, server, appliance, device, one ormore processors, circuit, etc. each of which may include a processor toperform functions as described and claimed herein. Examples of suchcomputer-readable storage mediums include, but are not limited to, ahard disk, an optical storage device, a magnetic storage device, a ROM(Read Only Memory), a PROM (Programmable Read Only Memory), an EPROM(Erasable Programmable Read Only Memory), an EEPROM (ElectricallyErasable Programmable Read Only Memory), Flash memory, and the like.When stored in the non-transitory computer-readable medium, software caninclude instructions executable by a processor or device (e.g., any typeof programmable circuitry or logic) that, in response to such execution,cause a processor or the device to perform a set of operations, steps,methods, processes, algorithms, functions, techniques, etc. as describedherein for the various embodiments.

§ 10.0 Photonic Performance Visualization Use Case

Network management is key to operating networks to perform variousfunctions such as fault analysis, performance management, serviceprovisioning, network device provisioning, maintaining the Quality ofService (QoS), Operations, Administration, Maintenance, and Provisioning(OAM&P), and the like. Generally, network management solutions areprovided through Network Management Systems (NMS), Element ManagementSystems (EMS), Craft Interface (CI), etc. via Graphical User Interfaces(GUI) for visualizing networking functions. Optical networks provide thephysical layer that interconnects nodes (also referred to as networkelements) to one another. For network operation, it is critical topresent a visualization of optical network operation for operators tounderstand the current situation, proactively address problems, ensurerestoration paths are available, etc. For example, a description of aGUI and network visualizations are described in commonly-assigned U.S.patent application Ser. No. 16/022,367, entitled “Multi-layer opticalnetwork management graphical user interface and visualizations,” thecontents of which are incorporated herein by reference.

Conventional GUIs for optical networks provide real-time visibility intonetwork performance and provide visibility into the efficiency of thenetworks. However, metrics associated with optical networks are complex,especially to visualize for operators. Optical networks in operationexperience failures such as, for example, fiber cuts, equipmentfailures, etc., and, responsive to such failures, the network isconfigured to reroute services on restoration paths. Various approachesare known in the art. It is critical for proper network operation tounderstand the availability of restoration paths.

The present disclosure relates to systems and methods for proactivelydetecting failures on restoration paths in an optical network andvisualizations thereof. Variously, the present disclosure includesadditional visualizations in terms of optical performance, such as, a)localization to visualize which sections or spans are large noisecontributors, b) what-if scenarios to monitor delivered Signal-to-NoiseRatio (SNR) of paths, and c) SNR-based routing to enable pathcalculation. Specifically, the present disclosure includes determinationand visualization of the optical performance of fiber spans andReconfigurable Optical Add/Drop Multiplexer (ROADM)-ROADM domains in thenetwork regardless of whether they are carrying traffic in order tohighlight underperforming links in a proactive way. This is accomplishedby measuring the current SNR margin on each and comparing it to aplanned SNR at the time the network was planned. This SNR margin andassociated categorization are available when interrogating individualfiber spans or ROADM domains but also summarized networkwide on adashboard to help the user proactively assess trouble spots in thenetwork.

The present disclosure provides a visualization of the absoluteperformance of spans and sections. This visualization could be used toprioritize routing, to determine network health, etc. For example, thevisualization, i.e., GUI, provides insight into which restoration pathsmay have issues due to degradation in SNR for the end-to-end path. Byexamining the restoration path overlaid on the spans, it is possible todetermine localization as to which spans are causing an issue.

Fibers and ROADM domains are applied a “heat” graphical treatment(graded color scale) on a network map to help the user visualize whereunderperforming, or indeed overperforming links exist in the network.Once users investigate a particular underperforming fiber span, they canview relevant associated optical characteristics about the links incontext. These include measured minimum SNR and planned SNR, the averagemeasured SNR, measured latency, and measured chromatic dispersion,distance, and fiber type. These are helpful to further characterize thestate of the fiber and may be helpful in explaining the measured SNR.

The SNR margin measurements are also used to evaluate the expectedperformance/viability of restoration paths in a photonic control planenetwork. Previous applications have focused on the transceiver totransceiver paths using measured line SNR, which only applies forcurrently active traffic. With the ability to look at other photonicpaths, regardless if they are carrying traffic, this gives the user theability to proactively determine if that path will be viable.Highlighting to users which photonic services have restoration pathsthat will not turn up because they are not viable enables networkoperators to proactively address these “silent failures” before anetwork restoration occurs and avoid an outage. The visualizationgraphically portrays each service with a visual representation of allpaths and whether it is viable or not based on the SNR margin. This canbe further differentiated from a path's unavailability due to a moretemporary cause, such as a network fault (e.g., red versus crossed-outin the visualization).

This list of paths can be presented in order of restoration preferenceso that the network operator can evaluate the level of risk—if the paththat is next in line for restoration is no longer viable, an outage willoccur, whereas if the problematic path is further away from thecurrently active path (e.g., marked in green), it is less likely to beencountered soon and gives more time to address the situation. Note, theuse of such visualizations is presented for restoration paths as anexample, a similar calculation can be made on demand for any photonicpath, independent of whether it is carrying traffic or not. This couldbe used by network planners to evaluate paths on demand for networkplanning or provisioning purposes based on real, measured data asopposed to planning data, which may very well be stale and no longeraccurate.

FIGS. 15-23 are various screenshots of visualizations for photonicperformance. In various embodiments, the screenshots are provided viathe management system 170, via the processing device 200, asinstructions stored in a non-transitory computer-readable medium, via acomputer-implemented method, and the like. The screenshots can visuallyprovide photonic performance based on the various techniques describedherein. The visualizations present optical layer performance informationfor an optical network, such as the optical network 100. Those ofordinary skill in the art will recognize that UIs can include variousscreens, windows, tiles, pop-ups, etc. and the various screenshotspresented herein are for illustration purposes, and other embodimentsare contemplated consistent with the descriptions presented herein. Thescreenshots contemplate use by a network operator, such as in a NetworkOperations Center (NOC) or the like, for performing OAM&P functions withrespect to the optical network 100.

FIG. 15 is a screenshot of a photonic performance dashboard 300. Thephotonic performance dashboard 300 includes example tiles 302, 304, 306,308, 310. For example, the tile 302 includes active alarms in theoptical network 100, the tile 304 includes custom alerts in the opticalnetwork 100, the tile 306 includes services provisioned in the opticalnetwork 100, and the tile 308 includes a number of network elements inthe optical network 100 currently under the management of the managementsystem.

The tile 310 provides photonic performance data. This includes a graphicstating all active service paths are operating within the expectedmargin. The tile 310 also includes a visualization 312 of fiber spanperformance, which is a bar graph displaying deltas from planned SNR(positive, nominal, or negative). The tile 310 also includes avisualization 314 for ROADM line performance that is similar to thevisualization 312. Finally, the tile 310 includes a visualization 316illustrating restoration in jeopardy. This displays a number of servicesthat have non-viable restoration paths.

FIGS. 16-18 are screenshots of a fiber span performance map 400,illustrating various features. The fiber span performance map 400includes a network map 402, which includes network elements 404,visualized as icons, and links 406 visualized as lines connecting thenetwork elements 404. There are various other aspects, such as ageographic map in the background that can give an operator context,e.g., a particular network element 404 is located in a particular cityor location, a particular link 406 traverses a set geography, etc. Thefiber span performance map 400 can include a visual key 408, whichprovides some indication of the performance of a fiber link 406. In thisexample, the visual key 408 includes colors which change according to arange of delta to planned SNR (dB). For example, dark green can be +2.0,whereas dark red can be −8.0 with different shades in-betweenrepresenting intermediate values. Of course, other types of visualindicators are contemplated, including different colors, icons, shading,cross-hatching, line weight, other line characteristics, fill, stroke,border, gradients etc.

Each link 406 can provide a visualization based on the visual key 408.For example, a link 406 a may be overperforming and is thus green.Another link 406 b may be underperforming and is thus red whereasanother link 406 c is neutral and is thus gray. In the example of FIG.9, the link 406 is selected, and a summary info tab 410 is displayed.The tab 410 displays current measurements with better than planned(positive delta) SNR, namely 24.9 dB minimum SNR (relative to 23.3 dBplanned) as well as an average SNR of 25.3 dB. Other measurements caninclude latency and chromatic dispersion.

FIG. 17 illustrates the selection of the link 406 c and the summary infotab 410 displayed with its information. The tab 410 displays currentmeasurements with values as planned (neutral delta) SNR, namely 25.3 dBminimum SNR (relative to 25.1 dB planned) as well as an average SNR of25.6 dB. FIG. 18 illustrates the selection of the link 406 b and thesummary info tab 410 displayed with its information. The tab 410displays current measurements with values worse than planned (neutraldelta) SNR, namely 18.4 dB minimum SNR (relative to 26.3 dB planned) aswell as an average SNR of 20.7 dB. Note, in each of FIGS. 16-18, theselected link 406 can include highlighting or some other visualizationso that it stands apart from other links 406 so a user knows the summaryinfo tab 410 is displaying information for that link 406.

FIGS. 19 and 20 are screenshots illustrating the expansion of thephotonic performance dashboard 300 illustrating a photonic service pathviability visualization 500. For example, the photonic service pathviability visualization 500 can be based on a selection, i.e.,“drill-down,” from the tile 310. The objective of the photonic servicepath viability visualization 500 is to present the health of opticalservices visually. The photonic service path viability visualization 500is presented in a table or tabular format with a list of photonicservices 502. Of course, other formats are contemplated. A photonicservice 502 can be a Sub-network Connection (SNC) such as in ASON orOSRP, a Label Switched Path (LSP) such as in GMPLS or the like. Thephotonic service 502 is a Layer 0 service providing capacity in someamount between two endpoints (e.g., ingress and egress ROADM nodes).

FIGS. 19 and 20 are screenshots that result from clicking an “expand”icon 325 on visualization 316 “restoration in jeopardy” of the photonicperformance data card 310 on dashboard 300. The basic idea is that allthe details that are summarized on visualization 316 of data card 310expand in place (replacing the dashboard). If the user chose to clickthe “expand” icon for the other visualizations on data card 310, namely312 or 314, their associated details would be shown instead. Note, oncea user has expanded visualization 316, they can quickly load any of theother visualization details from data card 310 by clicking along the topof the screen where the visualization summaries are presented. FIG. 19shows “restoration in jeopardy,” but a user can easily switch to“channel margin” details or “ROADM line performance” details by clickingtheir summary visualization across the top of the screen.

The list of photonic services 502 can include a service name, i.e.,something meaningful to an operator enabling them to correlate theservice to its owner. The list of photonic services 502 can include anoperational status indicator, e.g., UP or DOWN. This operational statusindicator indicates whether each service is up or not, and it caninclude colors, words, shading, etc. The list of photonic services 502can also include a capacity indication (e.g., 100G, 200G, 400G, ODUC2,ODUC4, etc.), a customer indicator (e.g., television, financial,consumer, government, content provider, etc.), endpoints (e.g., ingressand egress ROADM nodes), etc. The list of photonic services 502 can alsoinclude a home path indicator and a path viability visualization 510.

In an embodiment, the photonic service path viability visualization 500can be used to identify photonic services with restoration in jeopardyquickly. “Restoration in jeopardy” means that one or more next paths forthe photonic service are experiencing problems, such as from an SNRmargin perspective. A home path means a photonic service is on theoriginally provisioned primary paths. This can also be referred to as aworking path, etc. That is, the home path is the original path, such asthe optimal one (e.g., optimal is some sense such as minimaladministrative weight, etc.). When a photonic service is off the homepath, this means a switch has occurred where the photonic service hasmoved to an alternative path, for whatever reason, e.g., fault,maintenance, etc. A next path is an alternative path in the opticalnetwork 100 to route the photonic service between its endpoints.Generally, a photonic service should have one or more standby paths,i.e., non-home paths, protection paths, etc. The purpose of such standbypaths is to restore the photonic service when a previous path, such asthe home path, has issues, etc.

The present disclosure contemplates the processing device 200implementing the photonic service path viability visualization 500having access to or computing the possible standby paths as well ashaving the path viability performance, again either access to orcomputing the path viability performance. The possible standby paths arecomputed or known in advance, and such paths and the home path areranked in order, starting with the home path, next is a first standbypath, etc.

The path viability visualization 510 provides a quick and efficientvisualization to display the status of each photonic service's home pathand standby paths. The path viability visualization 510 includes a setof rectangles, where each rectangle represents an entire path (A to Z,where A and Z are the endpoint nodes) for that service to run on. Ofcourse, other shapes or icon types are contemplated. The key here isthere is one visual element 512 (here it is a rectangle) for each path,with the first visual element 512 being the home path, the second visualelement 512 being the first standby path, etc. Next, each visual element512 includes an indicator of the optical performance of that path, i.e.,its path viability. The visual element 512 can indicate a viable path(such as a solid box in this example), a current path on which thephotonic service is located (such as a border only in this example), anon-viable path based on measured SNR margin (such as a diagonal hash inthe box in this example), and an unavailable path based on a fault, etc.(such as a solid red box in this example, or some other color).

Further, the visual elements 512 may disappear if that particular pathno longer has the bandwidth available due to capacity changes in thenetwork. Even further, the visual elements 512 can periodically changethe indicator of the optical performance as updated measurements aredetermined, such as based on a refresh command 514, based on some timeinterval, etc. This is a real-time indicator. The visual elements 512highlight performance on each path, such as pass/fail based on margin,as well as path availability. Also, those of ordinary skill in the artwill recognize other types of visual indicators are contemplatedconsistent with the descriptions herein.

The advantage of the path viability visualization 510 is it provides adata in two dimensions in a convenient and efficient manner, namely anumber of restoration paths—based on a number of the visual elements510, and a state of the restoration paths—based on the indicatorsassociated with each visual element 510. Thus, a quick glance indicatesthe state of the network 100 for any given service.

In FIG. 19, a service 502A is highlighted and off its home path. Theservice 502A has 19 possible paths, of which 18 are viable. In FIG. 20,a service 502B is highlighted and on its home path. However, the service502B has only one standby (restoration) path, and it is not viable. Theselection of the service 502B allows a user to see additional details(see next few slides) for the service when clicking on a box 516 titled‘Details.’

FIGS. 21, 22, and 23 are screenshots of a map 600 and details 602 of thephotonic service 502B selected in the path viability visualization 510.Again, the photonic service 502B has two possible paths—its home path604 and a standby path 606, which is not viable. In FIG. 14, the map 600has the home path 604 highlighted and a subway map 608 visualizes thenetwork elements associated with the home path 604, expanded to includethe cards and ports the photonic service traverses. Here, the details602 provide the details of both paths, and the highlight in the detailsindicates the home path 604. The standby path 606 has a link 610 with anindicator 612 visualizing the span presenting a problem for the standbypath 606. Here, the indicator is a red circle with an exclamationpoint—any such indicator is contemplated.

In FIG. 22, the standby path 606 is selected, and the subway map 608changes to the standby path 606, which is not viable, as noted in thedetails 602. In FIG. 23, a summary data info pod 612 is displayed afterselecting the link 610 (or the indicator 612). The summary data info pod612 displays the current measurements of the selected span. Similar toclicking on the service to display the route, it is possible to click onthe span to see all the services with home and restoration paths thatmake use of that span. From there, the icon-based display of routesprovides visibility, whether any services are impacted.

The icon itself can be ‘clicked’ to display the route that itrepresents. The spans of that route can then provide the graphicalindication relative to plan as to how they are performing to helptroubleshoot and localize the issue.

Where a photonic service, such as the photonic service 502B, is injeopardy of not being able to restore, there can be a trigger to anapplication or user to recalculate the routes. A restoration path thatdegrades can otherwise represent a silent failure that is onlydiscovered at the time of restoration.

The various indicators in FIGS. 16-23 can be based on incremental SNR.For example, the calculation can concatenate the absolute penalties ofeach section within the network to determine the total SNR penalty of apath (including modern implementation noise) and compare it with therequired SNR of the modem to determine viability.

As described above, the same underperforming span can have differentimpacts on full paths, depending on how much margin is left. Note, it ispossible that some spans that are performing better than expected canmake up for ones that are not. When the user sees a span that is notproviding the expected SNR, it may or may not be of consequence. Bycorrelating that with the display of whether services are impactedprovides input on classifying the severity of the issue and where bestto ‘roll trucks’ to address the issues of consequence (‘roll trucks’means visit the site for on-site maintenance).

§ 10.1 Process for Optical Path Visualization

FIG. 24 is a flowchart of a process 700 for optical path viabilityvisualization. The process 700 can be a computer-implemented method, ina non-transitory computer-readable storage medium having computerreadable code stored thereon for programming a processor to performsteps or via the processing device 200.

The process 700 includes, responsive to obtaining measurement data froman optical network and determining viability of a plurality of pathsbased on Signal-to-Noise Ratio (SNR) and availability of the pluralityof paths, providing a User Interface (UI) that displays one or morephotonic services and a path viability visualization for each of the oneor more photonic services, wherein the path viability visualization, foreach photonic service, includes visual elements for available paths ofthe plurality of paths and an indicator associated with each visualelement indicative of path viability (step S21); and updating the UIresponsive to a change in any of the viability and the availability ofthe plurality of paths (step S22).

The process 700 can further include periodically obtaining themeasurement data from the optical network and determining the viabilityof the plurality of paths. The process 700 can further include providinga map view of all or part of the optical network, wherein the map viewincludes nodes and links interconnecting the nodes; and providing avisualization for each of the links based on a visual key, to indicate alevel of the viability thereof. The process 700 can further includereceiving a selection of a link; and displaying a summary of currentmeasurement data associated with the link.

The viability is based on the SNR and whether the margin is availablethereon, and the availability is based on whether the spectrum isavailable. The indicator associated with each visual element indicativeof path viability indicates any of viable, unavailable, current wherethe photonic service is using an associated path, and non-viable. Theviability of the plurality of paths based on the SNR can utilize anincremental SNR computation. The available paths, for a photonicservice, can include a home path and zero or more standby paths, with anumber of visual elements indicating the number of the zero or morestandby paths.

§ 10.2 Other Algorithms

Of note, the approach described herein is excellent for real-timecomputation. Also, there are numerous propagation processes that wouldaddress the incoherent (directly incremental) and coherent effects of afiber that could be utilized to model propagation behavior includingnonlinearities, in order from most pragmatic to least pragmatic (thelatter 3, and especially latter 2 methods are typically only reservedfor much more complicated devices than simple, low-index contrastwaveguides such as optical fibers): Split-step Fourier method (SSFM),Beam propagation method (BPM), Finite element method (FEM),Finite-difference time-domain (FDTD) method, and the like.

§ 11.0 Improve Physical Laver Modeling Through Aggregation of NetworkElement Calibration Parameters and Parameterized Behavioral Models

As described herein, factory calibration data can be used in the variouscomputations, that is many applications use generic calibrationparameters or possibly parameters provided by a manufacturer thatutilize a statistical representation of an ensemble of network elements(for example using averaged values, or values representing a certainpart of the distribution of manufactured cards). Parameter variationbetween amplifiers or other modules can be significant and failure toaccount for it places limits on the achievable accuracy of a propagationmodel. It is typical for a systems integrator to package and re-sellamplifier modules from multiple manufacturers under the same product.There can be material performance differences between different modules.

Network Management Systems and the like can combine network telemetrywith factory calibration data for individual network elements toestimate the linear and nonlinear noise that a channel would experiencepropagating through a fiber optic link.

Much attention is paid to nonlinear noise sources, but the linearamplified spontaneous emission (ASE) noise from amplifiers typicallyrepresents the dominant noise contribution by more than a factor of twoto one. Accurate modeling of ASE noise in telecommunication linksrequires sophisticated amplifier models which depend on calibratedamplifier parameters (which vary card-to-card) as well as the details ofthe amplifier operating mode. Furthermore, the ability to model anensembled concatenation of elements, including fibers, also requires thecapability to accurately model the gain blocks of the amplifiers whichcan rely on a subset of the same calibrated set of parameters.

In an embodiment, each module can include detailed factory calibrationmeasurements on a per-card basis to enable accurate modeling of the gainand noise transfer functions at any operating point. This set ofcalibration data can include noise figure (NF), dynamic gain tilt (DGT),and gain ripple which can be measured as a function of variousdimensions each (e.g.: frequency, gain mode, gain tilt, input power,output power, total output power offset, etc.). This amplifier factorycalibration data for each amplifier can be transmitted through anorthbound interface (NBI) of customer networks to enable noisecalculations at the orchestration level. As is known in the art, anorthbound interface is a data connection from a network element to amanagement system.

There has been a lot of work from third parties to develop propagationmodeling tools such as GNPy, which is an open-source model availableonline at gnpy.readthedocs.io/en/master/. Of note, the dominant errorsource in such models is inaccuracy in knowledge of one or moreoperation points of the network elements; for example: the amplifiers.This modeling requires proprietary data such as amplifier gain profilesand noise figures. Of note, amplifiers can be calibrated in the factoryand detailed parameters can be stored in each amplifier's cardcalibration table (CCT). This data can be exposed to a managementsystem.

The external SNR is the SNR on the symbols received by a modern afterremoving noise contributions from the receiver and transmitter. Accuratecalculation of the external SNR requires communication of moderncalibration parameters from the receiver as well as the transmitter tothe place where the calculation is performed. The concatenation ofincremental SNR contributions from the line system may be used todetermine the external SNR without requiring direct measurement withmodems. In this case, accuracy may be improved through the inclusion ofamplifier calibration parameters in the external SNR calculation.

The present disclosure can include calculating the noise in one or morespans of an optical telecommunications network using a centralcontroller that coordinates, and optionally performs the calculation.This calculation may include parameters extracted from one or moreamplifiers or other network elements. Parameters may include discretevalues, parameterized curves, look up tables, algorithms, equations etc.The parameters may be used to improve the accuracy of the calculation,and the parameter can be calibration data or the like that are storedwithin an amplifiers or other network elements firmware or in any othertype of memory (such as non-volatile memory that can be read or writtenby the firmware) during manufacture. Of note, the calibration parameterscan be transmitted through a northbound interface to the centralcontroller where they are aggregated for use in the calculation.

For amplifiers, the parameters can include one or more of the amplifiergain, noise figure, gain ripple, dynamic gain tilt as well as therelationship between those parameters and their sensitivity to operatingcondition. Examples include the variation of noise figure with gain aswell as the wavelength dependence of the gain for a given operatingcondition. Parameters may also include the presence of special featuressuch as the use of pulse width modulation on the amplifier pump lasersand the modulation parameters that are currently in use. The elementsmay include an EDFA, Raman gain amplifier, or other device such as aWSS, optical filter module, etc.

The parameters can be determined out of service as part of a calibrationprocedure and stored in the network element, card, module, orsub-assembly. An example of this would be factory calibration ofamplifiers and storage of parameters in the amplifier CCT.

The parameters are transmitted to the central controller through anorthbound interface using one or more communications protocols such asNETCONF, RESTCONF, Transaction Language 1 (TL1), Simple NetworkManagement Protocol (SNMP), gNMI, and the like. Industry standards suchas the YANG model as defined by groups such as the Open NetworkingFoundation, OpenConfig and OpenROADM are adapted to include support forthe northbound transmission of calibration parameters.

In an embodiment, sensitivity (parameterized) curves are transmittedthrough the northbound interface to enable a noise calculation. Thenoise or other calculation is performed within a network controller,NMS, EMS, etc. Also, the parameters can be aggregated by a networkcontroller (e.g., SDN) and transmitted to some other device for furtherprocessing.

Amplifiers are calibrated in the factory and the calibration parametersare stored in each amplifier's CCT. A noise calculation is requested fora given portion of a network. The central controller determines therelevant topology and the set of network elements that are present alongthe path. The network controller determines which parameterized curves,or portions thereof, are required for the calculation and polls thenetwork elements through the northbound interface to request therequired data. Firmware in each network element locates the requireddata and returns it to the controller in response to the request. Logiccontained within the network controller or on the network element mayhandle cases where data is not available by substituting the bestavailable data from other sources. The controller may also report theadditional uncertainty in the calculated result that is anticipated as aresult of the substitution. The noise calculation is performed withinthe controller and the results are returned to the process or user thatinitiated the request. In another embodiment, a controller can send acalculation procedure to the network element which performs thecalculation using the calibration data and returns a result to thecontroller.

Of note, there are existing approaches that suggest storing calibrationdata in modules, such as in commonly-assigned U.S. Pat. No. 8,233,215,the contents of which are incorporated by reference. The approach hereincontemplates taking this data from a module, through the networkelement, to a central controller, where it can be used to improve theaccuracy of a noise or other calculation. The present disclosureincludes taking the aggregate, and possibly post processed, data fromthe host (amplifier assembly) and transmitting it to a centralcontroller.

§ 12.0 Conclusion

Although the present disclosure has been illustrated and describedherein with reference to preferred embodiments and specific examplesthereof, it will be readily apparent to those of ordinary skill in theart that other embodiments and examples may perform similar functionsand/or achieve like results. All such equivalent embodiments andexamples are within the spirit and scope of the present disclosure, arecontemplated thereby, and are intended to be covered by the claims.

What is claimed is:
 1. A non-transitory computer-readable storage mediumhaving computer readable code stored thereon for programming a processorto perform steps of: responsive to obtaining measurement data from anoptical network and determining viability of a plurality of paths basedon Signal-to-Noise Ratio (SNR) and availability of the plurality ofpaths, providing a User Interface (UI) that displays one or morephotonic services and a path viability visualization for each of the oneor more photonic services, wherein the path viability visualization, foreach photonic service, includes visual elements for available paths ofthe plurality of paths and an indicator associated with each visualelement indicative of path viability; and updating the UI responsive toa change in any of the viability and the availability of the pluralityof paths.
 2. The non-transitory computer-readable storage medium ofclaim 1, wherein the steps further include periodically obtaining themeasurement data from the optical network and determining the viabilityof the plurality of paths.
 3. The non-transitory computer-readablestorage medium of claim 1, wherein the steps further include providing amap view of all or part of the optical network, wherein the map viewincludes nodes and links interconnecting the nodes; and providing avisualization for each of the links based on a visual key, to indicate alevel of the viability thereof.
 4. The non-transitory computer-readablestorage medium of claim 3, wherein the steps further include receiving aselection of a link; and displaying a summary of current measurementdata associated with the link.
 5. The non-transitory computer-readablestorage medium of claim 1, wherein the viability is based on the SNR andwhether margin is available thereon, and wherein the availability isbased whether spectrum is available.
 6. The non-transitorycomputer-readable storage medium of claim 1, wherein the indicatorassociated with each visual element indicative of path viabilityindicates any of viable, unavailable, current where the photonic serviceis using an associated path, and non-viable.
 7. The non-transitorycomputer-readable storage medium of claim 1, wherein the viability ofthe plurality of paths based on the SNR utilizes an incremental SNRcomputation.
 8. The non-transitory computer-readable storage medium ofclaim 1, wherein the available paths, for a photonic service, include ahome path and zero or more standby paths, with a number of visualelements indicating the number of the zero or more standby paths.
 9. Anapparatus comprising: a network interface and a processorcommunicatively coupled to one another; and memory comprisinginstructions that, when executed, cause the processor to responsive toobtained measurement data from an optical network and determinedviability of a plurality of paths based on Signal-to-Noise Ratio (SNR)and availability of the plurality of paths, provide a User Interface(UI) that displays one or more photonic services and a path viabilityvisualization for each of the one or more photonic services, wherein thepath viability visualization, for each photonic service, includes visualelements for available paths of the plurality of paths and an indicatorassociated with each visual element indicative of path viability; andupdate the UI responsive to a change in any of the viability and theavailability of the plurality of paths.
 10. The apparatus of claim 9,wherein the instructions that, when executed, further cause theprocessor to periodically obtain the measurement data from the opticalnetwork and determine the viability of the plurality of paths.
 11. Theapparatus of claim 9, wherein the instructions that, when executed,further cause the processor to provide a map view of all or part of theoptical network, wherein the map view includes nodes and linksinterconnecting the nodes; and provide a visualization for each of thelinks based on a visual key, to indicate a level of the viabilitythereof.
 12. The apparatus of claim 9, wherein the instructions that,when executed, further cause the processor to receive a selection of alink; and display a summary of current measurement data associated withthe link.
 13. The apparatus of claim 9, wherein the viability is basedon the SNR and whether margin is available thereon, and wherein theavailability is based whether spectrum is available.
 14. The apparatusof claim 9, wherein the indicator associated with each visual elementindicative of path viability indicates any of viable, unavailable,current where the photonic service is using an associated path, andnon-viable.
 15. The apparatus of claim 9, wherein the viability of theplurality of paths based on the SNR utilizes an incremental SNRcomputation.
 16. The apparatus of claim 9, wherein the available paths,for a photonic service, include a home path and zero or more standbypaths, with a number of visual elements indicating the number of thezero or more standby paths.
 17. A method comprising: responsive toobtaining measurement data from an optical network and determiningviability of a plurality of paths based on Signal-to-Noise Ratio (SNR)and availability of the plurality of paths, providing a User Interface(UI) that displays one or more photonic services and a path viabilityvisualization for each of the one or more photonic services, wherein thepath viability visualization, for each photonic service, includes visualelements for available paths of the plurality of paths and an indicatorassociated with each visual element indicative of path viability; andupdating the UI responsive to a change in any of the viability and theavailability of the plurality of paths.
 18. The method of claim 17,further comprising periodically obtaining the measurement data from theoptical network and determining the viability of the plurality of paths.19. The method of claim 17, further comprising providing a map view ofall or part of the optical network, wherein the map view includes nodesand links interconnecting the nodes; and providing a visualization foreach of the links based on a visual key, to indicate a level of theviability thereof.
 20. The method of claim 19, further comprisingreceiving a selection of a link; and displaying a summary of currentmeasurement data associated with the link.